I too have a small grass lawn and at one point it was filled with clovers and other weeds. It's base is mostly clay and topsoil. I tried the herbicide route before to no avail. They always returned. Unless you wish to kill your entire lawn by covering them up, there is no other solution but to dig them up. I have tried those weed clamps that do pull out small weeds effectively but not large and established ones.

Let me tell you how I managed to do this. First I watered the lawn so the ground is wet and weeds are easily pulled out. Next, I took a shovel and sunk it just a short distance away from the weeds and digging down to just beneath the roots of the weeds and I rocked the soil a bit to futher loosen up the roots. At that point, the weeds are easily removed. And with regards to dandelions, make sure to remove all parts of the plant as these will regrow from its roots. Sure it took a few days to completely eliminate the yard, but it was well worth that effort. Plus by loosening up the soil, I also managed to aerate my lawn at the same time. My lawn now looks rich and lush. I still have the odd weed or two, but these are new weeds and this time, a hand trowel easily does the job.

-now for the boulevard grass which sits on a rocky soil, this particular task is impossible. I hit rock hard earth and so digging is too difficult. So instead, I'm opting to remove the weeds by mass killing all the grass and weeds away. It takes maybe a couple of weeks to a month under completely black cover like thick newspaper layers. Once dead, i can reseed or resod the area. I prefer to reseed since we are close to fall and we can once again sow grass seeds.