This might seem too simple but I do get questions on this from time to time
The normal type of connection that uses different types of mobile data connection a in order to use Internet. Use s from 2G (GPRS) to 3G and the newer faster 4G (LTE). Connection speed depends on the network the phone connects to. 3G is most common yet, but LTE is getting more common. The “proper” 4G, LTE Advanced, is yet very new and can now in 2013 be found on just a few networks in the world.
WiFi, or wlan (wireless local area network)
Is a wireless connection to a access point, that’s often part of an internet router. Newer phones like HTC One can use the newer 802.11AC and connect to router using speeds around 450Mbit/s, but then you need WAN speed around 500Mbit/s for it to be really useful. Wifi got a sub-function called Wifi Direct that some phones got, HTC One X/X+ and One (and so on) got working wifi direct, you just need an app (like SuperBeam) to use it.
Near field communication, used for close contact communication. It builds on RFID. When used by Android Beam to “beam” information between two phones, NFC is used to connect the two phones but the the actual transfer is being done over bluetooth. Samsung uses a variant of this called S-Beam that uses wifi direct when sending the file, but that requires samsung in both ends.
Bluetooth, quote from Wikipedia
Bluetooth is a wireless technology standard for exchanging data over short distances (using short-wavelength radio transmissions in the ISM band from 2400–2480 MHz) from fixed and mobile devices, creating personal area networks (PANs) with high levels of security
it’s often used from hands-free headsets thanks to it being pretty low-powered, the newer iterations of bluetooth getting more and more efficient.