I'm not sure what you have in mind - how the roof will look. Assuming it's just a sloped platform...
Install a ledger board on the house for the length of the roof - make sure it is flashed and securely bolted to the house. Use joist hangers on the ledger to hang the roof rafters.
On the slab - how decorative do you want to be on the columns? You can use a 4x4 post - if you do, you should anchor it to the slab (ask at the hardware store how to do it - there's a bracket you can use.) Or you can use a larger Greek-style column - either a round pillar (premanufactured) or a square one made out of 1x6. If you use a wider, more substantial post/column with a 12" square base, you don't need to anchor it to the slab. The weight of the roof will be enough.
Run a beam from one column to the next to tie them together at the top. You can use rafter ties to attach the roof rafters (or you can cut birdsmouths if you know how to measure them.) You probably want to run a beam from the columns to the house, but you don't necessarily have to - depends on the pitch of the roof.
.. That might get you started - post again to ask clarifying questions.