You can buy selective weedkillers for lawns anywhere-or use a weed and feed.
I have the same problem and I am going to buy a fiskas weed puller.
Have a look at Verdone,which you make up into a spray/can and water on. i use it to go after those weeds the weed and feed might miss. Yellow trefoil is a particular problem later as it colonises the spaces left when other weeds die. You can't win!! The weed and feed will encourage grass growth remarkably. Use a drop spreader in preference as it doesn't woosh the weedkiller over your plants.
The cheapest way to get rid of weeds in a lawn is to crawl on your hands and knees, methodically across it, with a small kitchen knife or sturdy pen knife, taking the weeds out. Then scatter fertiliser and water in. Your lawn will soon look fine.
Bit pricey, but will last you for years, is a wolf-garten weeding knife. Sharp at the end, and rounded, about 6 inches long (at the business end), ideal for getting tap root plants like dandelion and thistle out. Make sure you get the metal one (I don't bother with plastic garden tools, as I tend to use lots of brute force and not sure if they'd snap). You will also need to buy a handle, I'd suggest either the 15 cms one if you're going to be working on hands & knees, or the one with a long shaft and a D-shaped handle if you prefer working standing up, or have mobility problems.
It's very good for chopping slugs in half, too.
It's only the weeds that keep my 'lawn' green in summer. Special thanks to white clover and self heal.