When using a small compact camera (the smaller and slimmer the better), you can either stow it in a pocket, hang it around your neck and shoulder on a cord (don’t hang it around your neck), or in a small pouch (clipped to your harness or rucksack, or on it’s on the sling). Having dropped a few cameras, and seeing partners drop cameras, I always keep my camera tethered to its case.
The best way to do this is to use a standard 2.5 mm or 3 mm bungee cord, or 3 mm Dyneema bungee cord (stronger), giving you enough cord that you can take photos without requiring too much cord length (less bulk and tangles). The camera end of the cord should be detachable, but using a tiny accessory krab (microwire gate), is not that secure, so using a 2.5 mm or 3 mm Maillon Rapide (Rapid-Link) is the best option, clipping it into a small loop of cord tied into one of the cameras strap holes (use the cord that comes with the camera or 2mm cord). Put a tiny bit of finger tape on the collar of the Maillon to make it easy to undo.
The other end of the cord should be tied into the camera case, and one method ties this into the case karabiner (use a small locker, like a Metolius Bravo, or a 7 mm or 10 mm aluminium Maillon), as this means if the case is ripped off your pack or harness (webbing fails), then the camera and case are tied directly into the krab.
A second option has the cord attached inside the case, as this allows all the cord to be stuffed away with the camera, which tends to be neater, and if you carry the cord bandolier style, it can result in a shorter length of cord.
The way to do this is to turn the pouch inside out and sew in a loop of webbing, with 10 mm grosgrain ribbon tape being ideal, being less bulky than full strength webbing (14mm nylon webbing is stronger, or you can use a piece of an old Dyneema sling). The loop can be hand sewn or sewn with a home machine, with ten to twenty stitches being strong enough for the job.