It sounds like you have separate itineraries, because Terminal 3 is exclusively for Emirates and Qantas, and Terminal 1 is for all other airlines.
Terminal 2 is generally reserved for low cost carriers.
To start off with - there are no visa requirements to transit between the three terminals.
However, as Terminal 3 is exclusively for Emirates - any checked baggage is transferred to Emirates (and possibly Qantas) flights. The only exception is FlyDubai which have an agreement with Emirates to transfer checked-in luggage.
So - to transit between Terminal 2 and Terminal 3 is possible if you are carrying a boarding pass / ticket for your onward journey. Simply follow the transit signs and ask the information desk for transit to Terminal 2 (or, just follow the transit signs for FlyDubai as they also fly out from Terminal 2).
Your baggage is a different story. If its only checked through to Dubai on Emirates; you will need to exit the terminal through immigration; collect your bags and then re-check in at Terminal 2.