Well, I almost always get the Great Library because it's my first priority, but I hardly ever manage to get more than one wonder in the ancient era (playing at monarch level).
For me, I found that if I chose one GW to go for from the start, I could usually get it. If I just tried to wing it, I usually got beat out on all of them, until at least the medieval era.
Here's what I do:
-> choose a wonder based on your civ's starting techs -- EG if your civ starts with alphabet, you're a step closer to the G. Lib and the G. Lighthouse, so they're good choices.
-> Designate a production city as soon as possible. More often than not, this is my capital city. If so, you obviously have to build a settler there, but other than that, all it builds is a temple, and if necessary an aqueduct (hopefully you'll have a city on a river though). Defense is shipped in from other cities, unless you have time to kill. Then you let it grow and leave the settler / worker building ot the rest of your cities. Make sure you build mines on all used squares in your prod city's radius as soon as possible.\
-> of course, you can't rush wonders in the normal way without a leader, but you can get a head start with a timed switch from a partially complete project. Check how long it will take to build the biggest improvement available -- say it's a marketplace at 9 turns. When the time left to discover the tech you need for your chosen wonder gets to 8, start building the marketplace. When the wonder becomes available, you'll have an 8-turn head start. Choosing a city other than your capital to be your prod city is an advantage here, as you can start building a palace in it. Make sure you don't accidently complete this project ahead of time! If you suddenly notice that you're ahead of schedule (EG your city grew in the meantime), you can just turn a citizen or two into entertainers to slow it down.
BTW, here's a (somewhat) risky but rewarding strat if you get a leader & want to rush a wonder with it. If you're already building a wonder somewhere, and there's another great wonder available (or will be soon), don't use the leader yet! Save it until your wonder is 1 turn away from being done. Then you can build two GWs in the same turn. The advantage is that you're much more likely to screw everyone else in the wonder race by robbing them of their fallback wonder, forcing them to waste their accumulated shields. You may refer to this tactic as Mr. Socks' Wonder Blitz
