The process of moving network has been designed to keep the time you’re without a service down to a minimum.
Even after you’ve given the network you’re joining your PAC code (see above for a more detailed explanation of PAC codes), so you’ll still be able to take calls and receive texts during this time.
When the transfer to your new network is actually happening, your service will be down for a very short period.
To test when the transfer has been done, simply insert your new SIM in the phone and restart it. If you’re got a service, you’re good to go.