How can I prevent water from pooling in the street in front of my house?
Most towns/cities will not be too happy with you, if you start cutting up their road. So you'll have to use a method that will be completely on your property.
Dump some dirt
The easiest solution would be to build up the area with a load of dirt.  Using a wheelbarrow and a shovel, grab some dirt from another location in your yard. If you can't find a place in your yard to take dirt from, you could always purchase some from a gardening/landscape/home improvement store.  Dump the dirt along the edge of the road until your hole becomes a hill, then feather it into the rest of the yard. Plant some grass, and grab one of @dbracey's margaritas and watch it grow.
French drain
A french drain would give the water a place to go.
Start by digging a trench right next to the road about 12&quot; wide, and 12&quot; deep (don't forget to call before you dig, so you don't damage any underground utilities). You want the water to drain away, so you'll want a drop of at least 1/8&quot; for every 1' in length. For example. If the drain will be 20' long, the end of the drain will be 2 1/2&quot; lower than the beginning. Next fill the trench with about 4&quot; of crushed stone, and lay your drain pipe in the middle of the trench. You can use either rigid, or flexible pipe.

Fill the trench to about 2&quot; from the top with more crushed stone, then finish filling the trench with topsoil. plant grass, and enjoy.
Concrete gutter
If you're familiar with working with concrete, and you like a more finished look. You could install a gutter, along the side of the road.

Just remember, you'll need the gutter to slope so water will run away.  It's probably a good idea to install a dry well or other drainage method at the end of the gutter, so the water has a place to go (unless you don't care if you simply move the puddle to your neighbors yard).