In the beginning I had a difficult time with counting outs and calculating pot odds. As with many things in poker, practice and doing is the way to learn. All I did was play 1 table and write down all of my hands, had a calculator and sat there and practiced counting outs and calculating pot odds...whether I was involved in the pot of not.
What happened over time w/ practice is that you start learning the outs, learn which ones to discount, and how the math works out. It probably took me a solid month to get quick at it. If you honestly put the time in, you will be surprised how fast you can do it.

This is a quick and dirty way to figure pot odds.....you take the # of outs times 2, then add 1, and this will give you the percentage of hitting one of your outs on the next card. Next multily that percentage by the pot and the bet you are calling to determine the maximum bet you should call.

For example you have A-Ko....the flop is 2-7-T rainbow for simplicity. You have put your opponent on top pair with a decent kicker....9-T or Q-T. You have 6 outs for the over cards to pair (you also have a backdoor str8 draw but lets ignore that) 6x2+1= 13% you will get an A or K on the next card. Add the pot and your opponents bet by 13% (.13) bet to determine what sized bet you should call. There are other considerations such as implied odds, or simply playing your stack and position aggresively in NL, but for now just practice counting outs and you will be able to do it quickly in no time at all.