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Toward the end, the shape of opponents' hands can be read by "counting" (playing out two or three suits and inferring the shape of the remaining one(s)).

In the beginning, one looks for more subtle clues. If a lead is fourth best, one might look in hand or dummy for lower cards to see if the leader might have a fifth or sixth. If opener has bid three suits they are likely to have a singleton or void in the fourth. If one defender has bid they probably have the bulk of the defenders' points; if neither has bid, the points are (probably) evenly split.

What are other ways to draw inferences about opponents' hands after hearing the bidding, and seeing one or two rounds of play?

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The opening lead often gives you some hints. Ask yourself why LHO chose to lead that suit and that card. You can also get information from later leads if the opponents win tricks early.

If the opening lead is a high spot against a suit contract, there is a good chance it is a singleton or a doubleton. If LHO is leading RHO's bid suit, is it a high, middle, or low card? The answer can frequently help you determine the distribution of the suit. If LHO leads low in a random suit, perhaps he is trying to avoid leading from honors in the other suits. Against NT, there is a good chance that the suit lead by LHO is his strongest (unless it is RHO's suit).

Ironically, you usually get more information from leads by strong opponents than leads by weak opponents, whose leads are a lot more random.

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