You're starting out with:
1TB: OS + games (I)
250GB: data + games (II)
and you want to end up with:
2TB: (I)
1TB: (II)
(You haven't said, but the assumption is that you don't have room to move (II) onto the 1TB drive.)
First thing's first, you should have some kind of external backup for your data, stuff you don't want to lose. You should have this anyway, you really should.
Next you need some software that can perform cloning and imaging of disks, e.g. Macrium Reflect.
Ideally you need some external drive with at least 256GB free. If you do, the sequence is this:
1) Copy all of (II) to external drive.
2) Remove 250 GB drive and install 2TB drive.
3) Clone (I) to 2TB drive.
4) Remove 1TB drive, move 2TB if desired.
5) Check PC boots from 2TB drive.
6) Reinstall 250GB drive. Reboot and check the system behaves itself. The longer you can do this (e.g. over days) the better.
7) Remove 250 GB drive, reformatting it first if planning to sell.
8) Install 1TB drive and reformat it.
9) Copy all of (II) from the external drive to 1TB drive.
If you don't have an external drive it's more fiddly, but you still should have your data backed up to the cloud. If you've no data backup at all, go and buy an external drive unless you really have nothing you don't mind losing forever.
Without an external drive:
1) Remove 250 GB drive and install 2TB drive.
2) Clone (I) to 2TB drive.
3) Remove 1TB drive, move 2TB if desired.
4) Check PC boots with 2TB drive.
5) Reinstall 250GB drive. Reboot and check the system behaves itself. The longer you can do this (e.g. over days) the better.
6) Copy all of (II) to the 2TB drive.
7) Remove the 250GB drive, reformatting it first if planning to sell.
8) Install the 1TB drive, reformat the 1TB drive.
9) Move all of (II) to 1TB drive.
When you reinstall the 250GB/1TB drives you may need to set the drive letters in Disk Management to get everything to work correctly. It's very important to boot from the 2TB drive without any other drives installed first though.