As we're not a graduated site, we can't have community promotion ads on our site at this point. What we can do is create adverts for G&FH that show up in the sidebar on other related sites in the SE network.
Let's create some ads here, and submit them to the Community Promotion Ad posts on the relevant graduated site. Ads typically need 6 upvotes before they are displayed on a site. Ads need to be 300x250 px, PNG or non-animated GIF, no more than 150 KB, and 1 px border if white background. Ads are reset annually, but there's no reason one can't be added mid-way through the year.
I think it helps to tailor the ads to the site they will appear on, rather than a generic ad. I've started one example for Biology SE to get the process going. Feel free to include designs or ideas for other sites we could advertise on. If you have an idea but no inclination to make an ad, myself or someone else may be able to make the ad. What other SE sites might it be useful to have an ad on?