New laptops have the wireless connection capability built in to them.

So if your router is also a wireless router as well as a wired router you should be set.
Does your router have a small antenna coming out of it?

Or post the brand name and model number and I can look it up.

If it is a wireless router = all you do is turn on the new laptop and it should find the connection for you.

But if there are security settings on the router that block wireless access then those would need to be changed or you would need the name of your home access point and possibly the password.
But that is only if someone set it up to be extra secure and the laptop can't "see" the router connection.