RGG FAQ Part 5 Section 2
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Counting whilst the game is still in progress is in fact extremely important, as it commands major strategic decisions, such as 'Do I need to invade, or is it sufficient to defend what I have already outlined ?'. It is said that the strongest players (like Minoru Kitani in the 60's) are those who know they are ahead, by e.g. 2 points, when their opponent is still wondering if he is ahead or behind.
The 'comparative' method: You look at the various territories on the board and compare them. Something like: 'My upper left is the same size as his lower left. My upper right is larger than his lower right, our sides are the same size: I am ahead'. This method is quick, but not very accurate. However, sometimes it may be all you need ..
The 'counting' method: You count and add the size of all your own and your opponent's territories. On the edge, you simplify by extending the territories straight down. Try to remember the individual sizes of the territories, this makes it easier to update your count later. This is of course more accurate but takes longer. Also, territory which is only very roughly sketched out (typically the centre) is very difficult to estimate. (Tip: normally, there are very few points in the centre. If the edges and corners are shared and all groups are out into the centre, there are probably not more than 5 points altogether for either player.)
If you cannot remember the individual territory sizes, try to remember how much of a difference to your original estimate the new position makes. (I.e. try to estimate a 'delta' score with respect to your last estimate, do not recount all the territories.)
If you find that, after you have counted your own score and your opponent's score, you have forgotten your own score, do the following: count your own score (example: 63 points). Remember 100 and start counting your opponent's score at 37. If his score then ends up smaller than 100, you are in the lead. (The trick is that it is easier to remember '100' or '50' than other numbers)
Don't forget to add komi, if any, to white's score.