What is a good way to get used to counting points?
The advice I have heard most is to count in pairs.  The human mind can easily count groups of around four objects, and so it may be beneficial to eventually move to counts of fours, but pairs tend to be easier in my experience.  Count a dead stone as one pair, and if you see a lone empty spot, just mark that in your mind and continue, removing the mark and adding a pair once you see another lone empty spot.

Once you have your count for one colour, either subtract that number from 50 (or 100, if there's a lot of empty room), or start counting down.  Otherwise, you are very likely to forget the score you counted, making you start all over again.

Another useful trick is to simply balance large pieces of territory against each other, and then count what's left;  this is less accurate, but in the mid-game speed may be more important and you may be unable to give good estimates, anyway.  Make sure to multiply the value of an area by the probability of the player keeping it;  a good way to do this automatically is to count in threes or fours when looking at large areas that are very likely to be invaded.

A fairly obvious trick is to count in your opponent's time; however, be careful that you still count the effect of your move before you play it (if possible), and not afterwards.  Especially in the yose, if you have time, try to count how many points a move will cost.  In many cases, you may find that taking sente may be worth more than responding to the opponent's move.

Finally, if you happen to have trouble keeping track of the score, consider learning binary;  it'll let you count to 1023 on your fingers, which should be enough for most games. :)