Q: How do you restore an old iPhone to use as an iPod without a sim card?

All you need to do is to connect the iPhone to your computer, open up iTunes, let it sync.

As you can see the iPhone in the devices list on the side bar of iTunes, right click on it and select backup.

After a backup is done, hit the restore button. It may download the latest version of the iOS and it may take a while.

After restore is completed, you will need the original SIM card to activate your iPhone inorder to use all it's features.

When your iPhone is restored it will ask you whether to set it up as new iPhone or restore from backup.

IF you don't want the previous data, you can select the option "Set up as new phone"

This should solve your question

You need to get the SIM card, you'll jus need it for activation, after it's activated, you won't need the SIM card.

If you don't have, borrow it from your friend for 1 minute and connect it to iTunes to activate it! After activated, you can remove the SIM card and you're good to go!