I can't add too much more than what big Uncle has said. While I haven't gone on our hunt yet, I've been buying points and researching for the last four years for a group of 6 of us.
Take the time and do your research. The Wyoming website offers allot of information on past draws, as well as hunters success, land access, etc. Make use of that website and all that it offers. Also, make phone calls. This can help you get a better understanding of what the public Access is really like on the units that you are interested in, as well as better information on winter kills and the local antelope herd.
If you think you want to do it in the future, start applying for points now. $30/year will get you a preference point. And will greatly increase your ability to draw into better units when you are ready to hunt. A couple of points can still go a long way. Although, just like every where else, its taking more points each year to draw better units.
We apply as a group. So each year the members of my group have bought a preference point each. They will average out your groups points. (If one person has 6 points and one person has no points then the two of you will apply with 3 points.)
One member has to get online and open the group application. You will get a group ID number to give to your party, and then they can join the group application using that ID. This allows everyone in the group to be drawn, or not drawn, together.
There is allot of information on the Wyoming website, and it's the place to start if you want to plan an antelope hunt.
Unfortunately the days of easy to get license, and lots of available land are gone. But I think a good hunt can still be planned relatively cheaply if you do your homework.
-Jake