This article is from the Go FAQ, by Morten PAHLE email@example.com with numerous contributions by others.
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.