Usage of なん　vs. なに
When do we use なん and when do we use なに? Is there any regulation regarding their usage?

Question

Answer

When following word is a counting unit, it always be pronounced as なん. 
何人(Nan-nin), 何歳(Nan-sai), 何分(Nan-pun), 何度(Nan-do), 何回(Nan-kai)

And if it is followed by a particle, merlin_codex is almost right.
何が(Nani-ga), 何を(Nani-wo), 何も(Nani-mo),
何の(Nan-no), 何で(Nan-de, Nani-de), 何と(Nan-to, Nani-to)
But sometimes, we say Nani-de instead of Nan-de, because Nande also means 'why', and in order to avoid confusion we may say Nani-de for 'by what'.
And in case of '何と何を組み合わせますか？(combine what and what?) 
'Nan-to Nani-wo kumiawasemasuka?' may be the logical reading, but actually many say 'Nani-to Nani-wo kumiawasemasuka?'. Both are acceptable.

Answer

The kanji is one alone -> 何. When placed before words that are starting with the "n", "d", "t" sound, it is read as なん, otherwise -> なに.