It depends what kind of species You are going to analyse in assemblage ( on macro, micro or nanno scale) and are you going to do their relative or absolute abundance, and what kind of diversity do you have (monofloral or rich in different species)...
Maximiliano's is the most practical answer... if you have got a spreadsheet with species counts (each row a species, each column a site or a sample), just copy and paste (edit >> paste) and follow the manual, you'll find the way quite fast!
Actually, it's very easy: you have to arrange your data with species (or your taxa) in rows, and samples (or sites) in columns. Then, you can perform all the analyses in the "Diversity" menu.
Some of these analyses work on each column (for example, "Diversity indices", or "Individual rarefaction"), whereas other consider all your data as a whole (for instance, "Quadrat richness", or "Sample rarefaction"); it all depends on your research interests!
Note also that, for "Beta diversity" analyses in PAST, first you have to transpose your data.