Steps after buying a used iPhone
Once you get your hands on the iPhone, put your SIM card in it, do a full reset, and after it restarts go through the initial setup phase - until you get to the main screen with the apps on it.

Make sure you have a mobile phone signal (3G or 4G or whatever). That will tell you that the phone will work with your SIM.

It will also have activated the phone during that initial setup.

If the phone was previously assigned to another iCloud account, it may prompt you for the password for that account during that process. If the seller does not have the password, hand the phone back because it's a brick. And probably a stolen brick at that.

After that, you're pretty much OK.