There are many ways to carry a camera. Most are supplied with a neck strap (and there is a non-slip shoulder equivalent, the UPstrap). Wearing a camera around the neck gets tiresome really quickly, makes you look like a goofy tourist, and potentially attracts the undesirable attention of thieves and would-be muggers.
I usually carry my camera discreetly inside a shoulder bag. A regular bag, mind you, not one of those obesely over-padded camera bags that are so bulky as to preclude walking around with them. You still need something to secure the camera, prevent it from slipping from your grasp and falling onto the hard pavement.
For pocket cameras, the wrist strap usually supplied will do just fine. You can get a tighter fit by attaching a cord lock (Google comes up with a bewildering variety of them) and reduce the risk of the lanyard slipping off your wrist. For some reason, only Contax had the sense to supply lanyards with a built-in cord lock.
For larger cameras, you need a hand strap. They are very common with camcorders, but unfortunately, very few camera manufacturers think of offering them as an option, or even provide bottom eyelets to make attaching them convenient. You have to hunt for third-party accessories and attach them using the tripod screw mount at the bottom of the camera.
For some time, I have mounted a cheap Sunpak hand strap on my Rebel XT. It does the job, but the plastic tripod mount is flimsy and unscrews all to easily, and the vinyl is not very pleasant to the touch. Another issue is that it precludes the use of an Arca-Swiss type quick-release plate. About a year ago, I wrote to Acratech, the people who make my ballhead and the QR plate on my Rebel XT, to suggest they drill an eyelet in the plate to allow mounting a strap, but never got a reply back.
I recently found out that Markins, a Korean maker of fine photographic ballheads, apparently took a patent on the idea and sells leather hand straps to go with some of their QR plates. Despite the princely price, I immediately ordered a set.
You have to unwind the strap to thread it through the eyelets on the camera and the QR plate, and back through the leather knuckle guard. This is fiendishly difficult to do if you don’t know the trick to it: wrap the tip of the strap in packing tape to produce a leader, and cut to a taper with scissors to ease insertion.
This strap works because the Rebel XT has a protruding hand grip. For a camera like the Leica MP, which does not have an ample grip (unless you attach an accessory grip), I use a sturdy strap liberated from my father’s old 8mm movie camera.
If you don’t have one of these lying around, you can always try one of Gordy Coale’s wrist straps, or if they lack snob appeal, Artisan & Artist makes ridiculously fancy (and expensive) ones for Japanese Leica fetishists.
I use a Peak Design hand strap on my Nikon Z7. It attaches to a standard Peak Design anchor at the bottom (in this case, attached to a RRS QR plate) and has a gate clip strap at the top that goes through an slot-type eyelet (or in this case a triangular split ring).