If you are playing in a suit contract (where a specific suit is trumps) then normally your opponents will lead one of the other three suits. The first thought that you could entertain is why did s/he lead that specific card. You canlook at your (including the dummys) holding in these suits and see which cards in each of the suits your opponents hold.
Possibly the first question you could ask yourself is why did they lead that suit. Of course if the auction has beencompetitive they likely will lead one of the suits they havebid. But if uncontested you can look at the cards they hold in those suits and try to determine what holding the leader could have to make that lead the most attractive one.
It is possible that the holding in that suit is suitable. For instance if there is king, queen and jack held, leading the king makes sense. It is also possible that the holdings inthe other two suits are less attractive. For instance say you are missing ace, king and queen of a suit. If it is not ledyou can assume that the leader does not hold ace and king or king and queen but more likely ace and queen or bare king. Certainly this sort of logic is not foolproof, but you can get a clue if you approach it in this way.
Personally I find much more success in figuring out what the opponents are up to by imagining what they are holding in the suits they dont lead. These inferences cancome in handy later in the game when there are decisions to be made concerning finding specific cards.
There are several reasons for leading trumps. If you andyour partner by the bidding seem to indicate that you aregoing to be trumping a dummys short suit it can be verydamaging for the opponents to attack your trumps at the beginning. If the bidding has indicated that you are in a four/four fit and you, as the leader hold four trumps, it can frequently be a good idea to lead them so that youreduce the trumping possibilities of the declarer as soon as possible.
If the opponents lead trumps you already have a clue as to what their holding likely will be. If you are missing an honor it likely wont be with the leader. If there is a suitwhich by all logic should have been led there will be some holding in that suit in the leaders hand that makes it unattractive. It usually is not difficult to figure that one out.
It is possible to write a book about playing to the firsttrick. It probably has already been done. I am not going toattempt this feat here. I merely wanted to admit that I amguilty of this basic sin as a bridge player and hopefully can help you avoid it as much as possible.