When the time rolled around for me to purchase a plane ticket to China, I had no idea where to begin. Now I feel sort of qualified to tell you about my experiences, and hopefully it can help you out.
The first time I came over, I felt overwhelmed and didn't know where to start. So many online travel sites! So I just had someone else do it! Travel agents can come in handy in this respect, because they do all the footwork for you. It was such a weight off of my shoulders to have someone just handle it for me. Travel agents in the US have been somewhat outmoded, but there are still some hiding out in the woodwork in the U.S. See if your more experienced friends (read: seniors) can recommend a travel agent to you, or just do an online search. Contrary to what I originally thought, travel agents get paid by their airline partners and do not charge you any cost for the tickets.
If you are feeling brave enough, you can try online airfare sites. I discovered that they were extremely easy and convenient to navigate. Most major travel sites directly link to each others' prices when you search for airfare. All the prices are provided right in one place, cutting down on the hassle of going to each sight individually. Most sites also had very similar prices, and a direct flight on any given day would only vary by a few dollars or so, so don't feel like you have to look at every travel site on the internet. When viewing ticket prices, make sure to note if the price includes tax or not.
This time around, I purchased my flight about 8 weeks ahead of my departure date from Expedia.com, and I felt like that I got a pretty good deal on a one way ticket (about $600 for a one way flight plus taxes, totaling about $850). Start monitoring websites about 10 weeks ahead of time, and just do a quick search once a day. When I was looking recently, prices started at about $1200 (tax included), but eventually came down to something more reasonable. Round trip seemed to be much cheaper than buying one-ways, so if you know when you are coming back, definitely spring for the round trip. Also, be ready to purchase tickets when you see a good deal; there is no reason to wait and worry and wonder if a better deal will come.
That just about covers it for my tips. There are not a whole lot of info here, because purchasing a ticket was actually much less mysterious and difficult than I anticipated. Just watch, wait, and the price will come down. If the price is right, buy it and be on your way! Go check it out and see how easy it really is.