The defining feature of a combination is that it is forcing: each of the opponent's replies is either forced or heavily restricted, which is what allows the initiating player to calculate the whole sequence in advance with confidence. Combinations typically rely on features already present in the position — an undefended piece, a weak back rank, a king caught in the center — rather than appearing out of nowhere.
Studying combinations is really studying the tactical motifs that compose them: pins, forks, skewers, discovered attacks, and deflections rarely occur in isolation in strong play, but chained together they can force a decisive result even from a materially balanced position. Solving tactics puzzles is the standard way to train the pattern recognition combinations require.
Good players habitually check candidate combinations at every move — "if I play this forcing move, what happens next, and is it forced?" — as a way of not missing forced wins and, equally, of avoiding opponents' combinations against them.