Sidewalks, paths or walkways serve one purpose. They lead your feet from one place to another. But if these routes are compromised by intrusive weeds it makes an undesirable impression on the expeditionist.
Prior to laying concrete, pavers, stone, wood chips or whatever surface you choose consider applying a layer of 8 millimeter black, polyethylene landscape fabric. You will find it much easier to control weeds before they get established.
If you have a sidewalk or driveway already paved and find troubled expansion joints, a urethane caulk will seal those areas preventing any unwanted weed growth. You can purchase a tube of caulk from any home repair center or hardware store for about $5.00. If cracks exceed 1/4 inch you will want to fill with a foam backer rod first then fill in with caulk.
Scrape or dig out weeds with a pavement weeder. A pavement weeder is simply a sharp, pointed tipped hand tool that fits into the cracks.
Some home made remedies for controlling weeds which provide great results is to pour vinegar, salt water or boiling water directly on weeds. These liquids will kill weeds by shocking their roots. However, be careful not to allow run-off to stream into nearby plants or grasses.
Herbicidal soap will do wonders but may require several applications unless weeds are discovered while they are young.
If you feel confident using chemicals, non-selective herbicides like Round-Up™ will do the trick. It may take several days before you see results but it lasts relatively long and may only need one additional application in a growing season.