Mow it with the blades set fairly high the first couple of times, and gradually reduce it down.
Don't cut it when it's wet.
Try not to walk on it when it's wet either.
If you mow the lawn about every 3 days, then you don't even need to use the grass box. The little bits just fall down and disappear into the mat of grass to decompose naturally. Cutting frequently also helps to suppress weeds.
In very long dry and/or hot spells in summer, don't cut it at all. It will go brown, but as soon as the weather changes and you cut it, it will go green again.
For the odd weed here and there, I usually cut them out with a vegetable knife. If your lawn is full of weeds, then you might need to take advice from a knowledgeable person at a garden centre who will sell you the right stuff to treat them.
If you do use lawn weedkiller, then leave it to work according to the instructions and don't compost the clippings, they need to go in the bin.