Hi Laura, no doubt you'll get many replies and probably many different favourite 'weeding regime's' b ut for what its worth, this is how i do it ! I spot spray perennial weeds with glysophate (carefully on a still day) or if your 'anti-chemical', dig them up ! As for annual weeds, the secret is timing, both weed size and weather. Firstly, try to do it when the weeds are small and secondly do it on a hot sunny day and you'll find that they just shrivel up.
My favourite tool for weeding is a very sharp draw hoe (the type you pull towards you) this way as you work forward your pulling the weeds away from the areas your working and i find you miss fewer weeds this way. Once clean, I mulch with woodchip, obtained free when my local tree surgeon is working in my area and they are pleased to have somewhere to dump these chippings.
These chippings very quickly go dark and for me its a cheap way to mulch !
My shrub beds are now quite mature so, I get very few weeds. I did spend alot of time prior to planting to make sure there were no perennial weeds and I'll be honest, i rarely get enough to compost bu if i did, I'd be quite happy to put them on the heap, bearing in mind you should only have about a 6" layer of 'material' and then I'd sprinkle a little soil in between along with a scattering of fish blood and bone just to get the compost heap working.
Finally, I think its important if you have a bad weed problem, to hoe at regular intervals, almost before the weeds can be seen, this way, especially at this time of year, these small seedlings once disturbed quickly disappear.
Lannerman