Do you have to BUY keywords for an Adsense website for them to show up in a Google search?

[me]

Sorry, a stupid question, I know.

If I have a website or blog that I partially use as a means of income via Google Adsense, do I have to actually buy keywords to use them on my site and for them to show up in a Google search? The reason I ask is because my website and blog doesn't sell anything, so pay-per-click ads (i.e. Google Adwords) are not what I'm going for and would not be cost efficient to say the least.

What other options are there to add keywords to my site or blog for free? Will they allow my site to show up in a Google search and, as a result, generate good traffic? All the videos and tutorials I see for Adsense always recommend using Adwords, but I can't afford to buy a bunch of pay-per-click keywords just to have a small chance that someone will click an ad on my site.

Thanks in advance.