Can I use my current sim card in a new mobile phone?

[magneto]

If I buy a new pay-as-you-go mobile (same as what I'm on now), can I just take out the sim card from the new phone and replace it with the one from my old phone? The mobile I want to get is the same make (Motorola) and network (T-mobile) as what I'm on now. I know you can get sim-free phones, but the model I'm looking at in a local shop isn't sim-free, just PAYG. Also, if I can use my old sim card in a new mobile should I put it in before powering-up the phone for the first time? Thanks