Which card combinations are required to score 29 points in a hand?
The only hand that will score a 29 consists of all four 5s and the Jack of nobs.
The scoring of this hand is nicely broken down in this Cribbage Corner post:

We score the 29 hand in the same way as any other: taking 15s first, then pairs, runs, flushes and nobs.
First count 15s. The Jack makes 15 with each of the 5s, that's 4 15s. Also, there are 4 ways of choosing three different 5s to make additional 15s. That's 8 in total, for 16 points.
Then pairs: there are 6 different pairs of 5s, for another 12 points. That's 28 so far.
There are no runs or flushes, so the Jack of nobs gives us a final point for 29.