According the classical book of Modern Greek Grammar by Manolis Triantafyllidis μπ, ντ, γκ have two pronounces: nasal and non-nasal:
1.1. In the beginning of the words: μπαίνω (to enter), μπαούλο (chest, trunk), ντύνομαι (wear), ντρέπομαι (to be embarrassed), γκέμια (reins), γκρεμός (cliff)
1.2. In the middle of the word after a consonant, and mainly for the words that have foreign origin: μπάρμπας (old man, uncle (informal)), τουρμπίνα (turbine), μπερντές (curtain in Turkish), φίλντισι (ivory), αργκό (argot), μπαμπάς (dad), μαντέμι (cast iron, from the word maden in Turkish, μπαγκέτα (baguette)
The most frequent case.
μπ and ντ: The first letter is pronounced as μ and ν as usual. The second letter π and t is pronounced as μπ, ντ, non-nasal as before. So αμπέλι=αμ-μπέλι (vineyard), Λαμπρή=Λαμ-μπρή (bright, but also Easter in a form), πάντοτε=πάν-ντοτε (always), πέντε=πέν-ντε (five).
γκ (or γγ): The first letter as ν. The second letter κ or γ is pronounced as non-nasal γκ. So αγκάθι=αν-γκάθι (thorn), αγκαλιά=αν-γκαλιά (hug), φεγγάρι=φεν-γκάρι (moon), Αγγλία=Αν-γκλία (England).
I hope it is clear.
The problem is which words are foreign and have to pronounced as non-nasal. Manolis Triantafyllidis included a list of such words: page 209 in the book (page 199 in the pdf file of the above mentioned Grammar): http://www.greek-language.gr/greekLang/files/document/modern_greek/grammatiki.triantafyllidi.pdf
Notice that this list is not full and has much changed with new words of foreign origin since that time.
It is a usual mistake even for the native Greek speaking to incline to pronounce the above μπ, ντ, γκ as non-nasal, obviously not knowing the above rules, much influenced by foreign languages. Even the newscasters on TV :-)
Yes, you cannot separate the letters and make two sounds, m then p as in English. What does happen, is, depending on what comes before it, μπ may sound as mb. Same with ντ, is always d, it cannot be separated, but may sound like nd. Don't worry about this little thing though, you'll pick it up as you go along.