A delicious dipping sauce. It's also used for... I want to say soba, which is a type of noodle ^^
つゆ is a type of sauce that normally has しょうゆ (soy sauce) and other ingredients like sugar, skipjack tuna (かつおぶし) essence, kelp (こんぶ) essence.
ん doesn't always make an 'n' sound, and is usually transliterated as 'n' or 'm' (in my experience, at least, I've never seen anything else) depending on how it sounds in the word. The wikipedia article about it is pretty good, albeit short, but I think that the most important thing is that ん is pronounced [m] before m/b/p. Hope this helps ^^
N and m are slightly interchangeable in japanese. Not always. Its the letter that comes after the ん. I.e. the P that comes after requires the softening of the ん to become more M like...
it's really rare, so just remember its this way on tempura and you'll be great. most of the time its pronounced "n"
This rule about "n" brings to mind "September" by Mariya Takeuchi! Give it a listen. It's an upbeat sad jam.
The pronunciation is closer to "sempai", but using modern Hepburn romanization it would be "senpai".