Q: How to add new computer to time machine

I'm very confused about all this. I bought a time machine and I backed up my old Macbook to it. Now I have a new Macbook Pro and want to keep the info from the old computer on the time machine as some files didn't get transferred. But now it will not recognize the new Macbook Pro. I bought a thunderbolt adapter and ethernet cable so I could connect it to the time machine but I do not see any recognition on the new computer. What on earth am I doing wrong. I'm not great with technology- probably pretty obvious - but very frustrated. Thanks for any help possible...