Compost all your weeds except bramble
The only weed I do not compost is bramble. I am not fond of prickly plants and so this is the one exception to my rule of 'compost everything from the garden'
Dandelions and docks have large tap roots and these need to be killed before adding to a normal compost bin. For this I use a turned inside out old compost bag. The inner surface is normally black and this on the outside will absorb plenty of sun and cook the weeds inside.
I keep a brick or tile on the top of the bag to keep it shut.
If you can shred materials before composting then they will break down faster.
Grassing cuttings and newspaper can be used to make compost