This is a very important time for your lawn- how you treat your lawn right now will set the tone for how your lawn looks for the next 6 months.
First, you NEED to address any weeds that have already emerged from the ground. These are cool season weeds such as chickweed, henbit, etc. These are easy to control RIGHT NOW with a broadleaf herbicide treatment. If you wait another month when these weeds are in full bloom and growing, they are much more difficult to control.
Next, you want to apply a pre-emergent herbicide (crabgrass preventer) to the lawn before soil temperatures reach 55 degrees (crabgrass can germinate once soil temps reach 57 degrees). As I write this on 2/28 soil temps are still in the upper 40's so we still have a few weeks of being in the window. Typically late February to mid March is a good time to do this treatment. Its a granular application that combines the herbicide with fertilizer to provide a feeding for your existing turf.
Other considerations to address are taking care of any bare spots in the lawn. If seeding is required, you want to do that in early February so you can still get some pre-emergent out in late March/early April. Keep in mind though, you won't have the best protection from crabgrass is you take this approach.
If you have issues with poa annua weeds in spring, well there really is'nt a great approach to fixing at this time of the year. If it really bothers you and don't mind paying the extra money, you can re-sod these areas. Otherwise, you should just live with it for another 6 weeks until it goes away on its own.