I bought a new house in December and my yard is full of weeds. How do I start growing grass?

Depends on

How many weeds you got
How quickly you want results
How phisical you want to get with the project
What type of soil you got underneath

If your yard is truly full of weeds, then you'll want to kill them before trying to grow grass. For most new lawns, you just ignore the weeds at the beginning, start growing grass and then kill the weeds after the grass has grown enough that you have had to mow 2 or 3 times.

If your soil is hard on the surface then you would be wise to rent a seeding machine that slits the ground and plants the seeds in the slits. If the soil is loose, you can use the machine or spread seed with a spreader. Fertilize with a "Starter" type fertilizer and then cover it with straw.

Either way you need to keep the surface of the ground moist by watering lightly 2 times per day until the seeds sprout and the seedlings are about 1" high. Then you can back off to watering once per day. The objective is to allow the roots to develop to the point that the grass can survive between normal waterings or rainfall.

Once you have mowed 2-3 times, then you can kill the weeds. Use a weed and feed fertilizer or fertilize separately and use a liquid fertilizer.

Good luck.