How can play my old games on my new Nintendo Wii U console?
You better learn fast, because that's all you will be playing. Nintendo released the Wii U with no game developed FOR the Wii U. The first real Wii U exclusive is Pikmin which doesn't come out for 6 months.
Yes you most certainly can play Wii console video games on the Wii U, just a few things you will need and need to do before you can though.
You can't actually use the GamePad to play those video games, so you will still need the Wii Remote, which you have to sync with the Wii U, and also any other Wii console accessory such as the Nunchuk, and also make sure that the Sensor Bar is attached to the Wii U too.
Then all it takes is just clicking the Wii icon on your GamePad and the Wii U will be switched over to Wii Mode and you can begin playing your Wii console video games there.