Simple answer: basically the same as what you would do for 2 colours. Setup the voltages correctly with an unstained sample, check if they're not too high with your single stains, then acquire your single stains and compensate. The compensation matrix is of course much larger with 8 colours than with 4 colours, that's why modern flow software can often do it for you.
More complicated answer: the more colours you have to compensate in a single channel, the more resolution you are going to lose in that channel. This can be very problematic, up to the point where you may lose all the signal on a dim population. That is why you should select fluorochromes which have as little overlap with each other as possible, and you should put the antigens which are least expressed on the fluorochromes with the brightest signal. Antigens with high expression (e.g. CD45) can then go on dimmer fluo's.