Kalven,
It is remarkably easy to book air tickets on-line. You already have the 1st ingredient - an on-line computer of some sort, or you couldn't have posted here. The only other thing you need is a valid credit card.
The airlines have their own sites -
www.delta.com,
www.aa.com (American), etc. To find one, just do a search on the airline name. You can book directly on them. Just find the flight you want by entering origin, destination and dates, and click on it. Then keep following instructions.
Then there are the more general sites -
www.travelocity.com,
www.expedia.com,
www.orbitz.com,
www.priceline.com, etc. You can book directly when on them, just like the airline sites.
Another category is even more general -
www.kayak.com. It searches lots of sites, and comes up with many options. Then you link from that site to a selected actual purchasing site.
If you post a specific trip you want to take, I'm sure somebody here will help you if you get stuck in the process.
As far as planning trips,
www.farecompare.com and matrix.itasoftware.com are very useful.
Why don't you post a little about just exactly what you are trying to do and then you will get a little more specific help. Where and when you want to travel? Why? ?? I necessarily had to be very general.
Romelle