New Hampshire splits its 24 pledged delegates into four pools - one for each congressional district, and two statewide (this is sometimes conceptualised as three pools, with the statewide pools combined, since this makes the number of delegates in each pool equal). A candidate needs to achieve 15% of the vote in a given pools area in order to gain delegates from that pool.
Each congressional district is given eight delegates to allocate, and eight are assigned based on the statewide vote. The statewide delegates are split into two pools. There are five "At-Large" delegates and three "pledged Party Leader and Elected Officials (PLEO)" delegates. This can produce some odd results due to rounding, as can be seen in this example from Frontloading HQ
If Candidate X receives 25 percent of the vote statewide and Candidate Y is the only other candidate above 15 percent with a 20 percent share of support then only that 45 percent total will apply to the allocation of the at-large and PLEO delegates. Those two candidates' total votes will be the denominator in the allocation formula. Candidate X would end up with 56 percent of the statewide delegates while Candidate Y would take the remaining 44 percent.
In New Hampshire under this scenario:
At-large (5 delegates)
Candidate X would be allocated 2.778 delegates [= 5 at-large delegates * .556] -- rounds to 3 delegates
Candidate Y would be allocated 2.222 delegates [= 5 at-large delegates * .444] -- rounds to 2 delegates
PLEO (3 delegates)
Candidate X would be allocated 1.667 delegates [= 3 PLEO delegates * .556] -- rounds to 2 delegates
Candidate Y would be allocated 1.333 delegates [= 5 PLEO delegates * .444] -- rounds to 1 delegate
There are no extra delegates awarded simply for gaining the most votes.