The most obvious way is to pull out the weeds, which should be easy after all this rain.  However if you haven’t the time or inclination for weeding, a dose of Glyphosate at 3% will do the job on most things.  Once you have done the weeding there are several measures you can take to try and ensure they do not return. It is a good idea to hoard all your old newspaper and cardboard over the year to put down on the ground between your plants to help suppress weeds.  This will both insulate your soil and stop the light from germinating any seeds.  

Once you’ve placed the paper 5-10 sheets thick over all the soil, simply cover the newspaper with 100mm of good quality mulch (i.e. Mega Mulch) and the result will be a warm weed free root zone ready for the cold of winter and the subsequent spring growth.  If you have no newspaper, weed matt is an alternative, but make sure it is spun-bonded and not woven, as the woven material does not allow adequate air and water to penetrate the soil, causing it to sour.  The warmth is important because it allows beneficial bacteria and worms etc. to keep working and making your fertiliser naturally.  

If you want to know what a weed is then that’s a good question because more old landscaping plants become new weeds every day.  Basically if it grows really well without any help and you didn’t plant it, it’s probably a weed.