Weed management is a huge topice.
1. Annual weed, these weed die in winter and need seeds to come up every year.
Pre-emergent herbicide don't kill any grass or weed, it only prevent ALL seeds from sprouting. You should spray pre-emergence herbcide every three month from spring to fall in order to stop weed from coming up, because the seed sprout all year except winter. Some weed specifically sprout in the fall and spring pre-emergent herbicite is too late for them.
2. Perennial weed, only wide spectrum herbicide will kill these weeds, but then you will kill your lawn as well. These weeds don't need seed to come back every year, your only option is to hire someone to remove them one by one.
If the weed already came up, you need to use post-emergent herbicide that kills the plants. Of course you don't want to kill grass, so the post-emergence herbicide only kills broad-leave weed (寬葉草),but not all weeds are broad-leave, so post-emergence herbicide cannot kill all weed without killing the grass.
So if you have grassy weed that are perennial, your only option is to hire someone to dig it up. I am talking about crabgrass. It's a headache.
I think you should just keep paying TruGreen. You don't want to deal with this headache.