For a blog or a site which isn't selling a product, advertising is the best way to make money. Advertising with Google AdSense is easily the best choice. (AdSense is the opposite side of the AdWords program.) Most people report that it pays far more than other advertising programs.
Yes, WordPress on FatCow hosting allows AdSense advertising.
Google only lets in completed sites of reasonable quality. Because of this, and because your site will have no visitors to begin with, you shouldn't try to set up advertising on a site during its first few months.
This is a typical AdSense block of ads that might appear on your site. This is one of the largest ad sizes. It contains four ads. Ads can also be pictures.
You put AdSense ads on your site, and whenever someone clicks on them, Google pays you.
Because you don't want to do this now, I'm not going to go through the details of setting up AdSense. You simply sign up with Google AdSense, then install one of the many AdSense plugins, inside your WordPress control panel.
With AdSense installed on your site, the Google "robot" then reads your site, to work out what your site is about. It then adds to your site relevant ads that it thinks will make you the most money.
Only some of your visitors will click on the ads on your site, but if you average it out, you can expect to make about 1-10c for each person who comes to your website. This depends heavily on the topic of your website. If your site is related to something commercial (like an amateur photography site or a blog about green energy), you'll make more than a site that's not related to anything commercial (like a jokes site, or a poetry blog).
Please note that you need to be very big, in order to organise your own advertising deals with other websites or companies. Thousands of visitors a day is probably a bare minimum. You can't sell advertising on a new site with no visitors.