can you put a tmobile sim card in a non tmobile phone and will it work?

okay i have a tmobile phone. i had the tmobile tap, the phone however all of a sudden stopped charging out of no where, & i tried three diferent chargers, so it had to be the phone, i took it to tmobile and they said they couldnt fix it. soo, i am now using my moms old phone that she accidentalyy slammed in the car door so i can only see half the screen, i cant see texts at all. my mom told her friend that this happend and she said that her son has a new phone and his old phonee is just laying around the house and works perfectly fine. but she never told me what brand it is. i have a tmobile sim card. can i put my sim card in a NON tmobile phone, like can i put my tmobile sim card in a verizon, at&t, cricket, sprint, or any other brand phones? If i can will you tell me what brands I can use to do this.
how do you unlock it? like i know my password for my sim card. & i can ask him the password for the phone. is that all i need or is there like another password that you need to unlock it like from the phone company or anything? say my mom had the env3 from verizon and she got a new phone and gave me that one, could i put my sim card in her env3. like just that and just use it, and im done. or what? lol.

You can use your T-mobile sim in unlocked GSM phones only. GSM networks include AT&T,T-Mobile,Vodafone etc. If you have a locked GSM phone you can approach the network provider or Mobileunlocksolutions.com and get the permanent unlock for the network lock which otherwise you cannot do it by yourself. Once unlocked you can swap simcards easily.