There are some basic confusions in this quesiton. Platforms like WordPress or Blogger do not pay. Ad schemes like AdSense do.
"Skewed" is right. The median blog probably makes $0. There are plenty of people who make 6 figures, but they represent probably less than 1% of the blogosphere. If you want to make 6 figures, you have to pick your topic very carefully for financial potential rather than personal interest, and work at it with the same 90-hour/week drive you'd put into a six-figure paycheck drive.
If you want to write about something you care about (and it's not a self-indulgent personal journal) the typical topic, if blogged well, can probably mature to a $10,000/year income stream at the 10 hours/week effort level. So about equivalent to a low-paying part-time job.
In other words, this is not a get-rich-quick path. The average blog will take around 2-3 years to mature. The fastest ones can mature in less than a year. The slowest ones may take 4-5 or more years even with the best execution. It all depends on the topic. You can accelerate the growth curve in artificial ways, but you'll pay the costs later (by artificially shortening the natural lifespan of your blog). I prefer what I call slow marketing: growing a blog at its organic, natural and sustainable rate of growth. By this criterion, my blog is a pretty slow-maturing one. It is just starting to mature, 4 years after I started. Another way to interpret this is: if a blog is your escape from the grind, start one a few years before you think you'll need the escape pod.
You should also keep in mind that like any other product, a blog has a natural lifespan depending on topic. I've grown mine with the hope that it will live as long as I myself do. So grow your blog at a rate commensurate with the lifespan expectation. If you think the niche will disappear in 2 years, it is stupid to plan a 4-year growth path. Try and optimize for NPV lifetime revenue, not isolated months or time-to-maturity.
There are two broad revenue types, direct and indirect. Direct income derives directly from blog content and requires no additional marketing effort. Indirect uses the blog as a marketing channel for other revenue, and requires conversion costs. In general, direct is much smaller than indirect. I'd say around 20% or less. There are categories where that can be reversed.
Direct is a fairly well-understood formula by now. You still have to think, tweak and optimize, but mostly it is execution and avoiding dumb mistakes. The hard part isn't the "make money" part here. It is writing (or drawing or podcasting) quality stuff week after week. In the direct game, 90% of success, as Woody Allen said, is just showing up.
For the make-money part, if you are smart, this answer plus a couple of months reading a site likeproblogger.net is enough. If you like more structured advice, a Dummies book should do it. If you like being spoon-fed, there are plenty of make-money-blogging online courses out there.
The top few, in reverse order of lucrativeness for me personally:
CPC: The baseline way to make money is AdSense. It took me 2 years to get to my first $100 paycheck from Google AdSense. Then 6 months to make my second $100. Then I turned the thing off. It isn't worth it unless you are writing something like a blog about a lucrative product category like digital cameras or the drug industry. You have to experiment to find out whether it is worth it for your blog. AdSense is the major cpc channel. There are others. Be aware that running prominent ads annoys readers, so there is a definite tradeoff.
CPM: cpm ads are far less popular at the low end and in fact I don't know of any automated one you can sign up for. I've run a few for about $50 a month each on a few popular posts. The advertisers sought me out. That's typically how this works. Once you hit a certain size, people will start reaching out to you with offers. Most are worthless. Some are fine. This is really worth it only for a very high traffic blog. Or for high traffic corners of medium traffic blogs. Beyond a point, if you want to do it this way, you need to go solicit ads from the right advertisers directly. Relying on the middlemen to find you gets you too little money. I had no energy and haven't pushed this.
Tips: I use the "Buy me a beer" plugin for wordpress (set to "coffee" instead of "beer"). There are many other such tipping-based schemes. This is my favorite because the psychology ("buy me a beer" instead of "make a donation") is done right and is 3x more effective according to the plugin-author's stats. This brings in $30 or so on a good month, $100-$300 in months where I have a viral hit.
Affiliate: This is the only channel I've truly stuck with, and only Amazon.com. This channel has grown with my blog, and these days I get somewhere between $80 - $200/month on average. This is because one category (books) is very well-aligned with my site. You have to experiment a lot to hit paydirt here. A friend pulls in more than $1000, also from Amazon. Be aware that currently in California, this program is suspended due to some wrangling between Amazon and the state government. To explore a broader array of affiliate schemes, try shareasale.com. I had no success with it.
Sponsorship: You can rig up simple paypal buttons or Amazon donation widgets to ask directly for sponsorship. This is only worth doing once you get feedback from readers that shows that there is significant reader loyalty and trust. They have to believe that you are writing for the sake of writing rather than for other motives.
Other: There are other direct channels I've made a conscious choice to not use. The most important one is simply the freemium model, with a "member's only community" and extra content. I am fine with this for high-value commodity content (news) or transactional types of content (teaching for example), but for most types of content I think this goes against the spirit of blogging and also makes very little marketing sense. You annoy readers, create an artificial barrier between paying/free members (remember, the value of a reader has almost nothing to do with how much they pay, and everything to do with the thoughtfulness of their commenting, the sincerity and enthusiasm of their support in word-of-mouth, etc.). I do like a version of this though... paid events.
I think it is very important to get the direct revenues up as high as possible: it is income insurance of sorts. And the content turns out far better if you try to make it pay for itself (otherwise it inevitably slides down the slippery slope from intrinsic value to content-marketing to open shilling for customers for other products/services). Try to get at least 15% of total revenues directly.
Indirect is harder and more lucrative. The potential upside is limitless, and at some point the blogging might even become a dispensable sideshow. But if you dive into indirect, you're no longer just a blogger. You are running a small business, and have to think like an entrepreneur. A bootstrapped-entrepreneur who happens to be starting with a live sales channel instead of a paper napkin and a pitch deck, but an entrepreneur nevertheless.
I am a relative novice at the indirect game. I've made decent money off 1, 4 and 5. I've done, but not made any money at, 2. I've not yet attempted 3 or 6.
Books: I've written a book. One of the most rewarding things you can do in your life. Financially (especially if you self-publish), spiritually, market-strategically.
Speaking/Workshops: I've done a few events. It's a whole other game. A successful blog is your ticket into Level 1 of this game, but then you have to learn this game as well.
Teaching: Done well, this is probably the most accessible and lucrative ways to make money off a blog. If you offer a course, virtual or in real life, anywhere from an afternoon to several weeks, you can make lots of money. If you are willing to prey on the gullible, you can practically mint money with feel-good motivational/12-step/get-rich-quick type content. I unfortunately have higher ethical standards than is probably sensible, given my financial situation, and therefore haven't yet come up with anything I'd feel comfortable charging for. I am playing around with a few ideas.
Freelance Writing: A blog is evidence that you can really build an audience. At some point, you'll have enough evidence that the freelance writing offers will start coming in. You should get a sense of your writing speed (finished words/hour) and convert everything into a per-word rate. The money can range from less than minimum wage on the low end to probably about $2/word at the high-end (web celebrity, not real-life celebrity, which is worth far more). Most clients pay per post. Some pay per word. Some pay per hour. You can get into this game today and make money immediately if you start with the content farming industry, but that is an extremely dumb thing to do. Freelancing is only worth doing, money-wise and satisfaction-wise (i.e. if you want to actually enjoy the gigs) if your own self-branded writing has a certain amount of validated popularity so you can charge a premium over other equally skilled writers. Even if you don't want your own blog at all (there are no good reasons for a writer to take this position IMO; it's like saying "I don't want a personal bank account"), it makes better sense to write quality stuff as an unpaid guest blogger than to write SEO-bait for the content farms. Even if you are destitute and hungry, you should probably try panhandling before writing for content farms. The pay is comparable if you can panhandle with a decent tearjerker pitch.
Consulting: this is the most loosely connected channel. The blog serves as a lead generation mechanism and lowers your marketing costs considerably (in business terms, I'd say SAG for a general consulting business probably runs around 25%; with a blog, if the blogging makes enough direct revenue, the lead-generation function is merely a nice free side-effect, and your SAG falls to maybe 10%).
Products: your blog's success may, upon analysis, turn out to represent market demand for things beyond writing. In other words, it may be pull evidence for products that don't yet exist. You can partner, or by yourself, produce those products and sell 'em to a ready-made audience. This is basic line extension. This has to be very carefully done, since you may misinterpret your blog's brand position with respect to that demand. If your brand is about unbiased reviews of digital cameras, and you end up with great ideas for the design of a really good new digital camera, you'll have to choose: do you want to give up the brand equity associated with unbiased reviews in order to throw your lot in with one camera? In other cases, things are simpler. If you write about personal financial management and offer a freemium calculator around your own ideas, that should be a natural line extension of the brand.