Again, there are a number of different types:
* Down shifters are mounted on the down tube (that connects the front tube with the bottom bracket). They are on their way of becoming obsolete, but are still the cheapest option. They are inconvenient because they require reaching down, which is difficult to do when braking or accelerating hard or riding in difficult situations. A variant that is mounted on the stem is found on very old and cheap bicycles.
* Bar-end shifters are mounted at the ends of drop handlebars. I haven't used them much and find them less convenient than Ergopower and STI brakes because I don't often keep my hands at the handlebar ends where I can't reach the brakes. They are popular on touring bicycles.
* Campagnolo Ergopower is a system for drop handlebars that integrates the shifting levers with the brake levers. This means you can control everything without moving your hands. There is one lever mounted behind the brake lever that tilts sideways to shift down, and a thumb button on the inner side of the body to shift up. Up to three gears can be shifted down, and any number of of gears can be shifted up with one lever action. The levers become less noisy and hard with time. Both brake and shift cables run along the handlebar under the handlebar tape. This is the system that I prefer. They also come with Campagnolo's spare parts availability - it's not going to be a problem to buy and install a replacement spring three years from now, when Shimano won't even remember what they sold six months ago.
* Shimano STI is similar to Ergopower, but there is no thumb button. Up-shifting is done by pushing the brake lever sideways. This is why I prefer Ergopower - it makes me feel more in control because the brake lever doesn't go in all directions when I hold it with two fingers to be ready to brake. Also, STI has cables connecting to the inside tip of the lever that are not tucked safely out of harm's way like with Ergopower.
* Other types are available for mountainbikes. I have not used them.
On road bikes, the shifter cables run along the down tube, on the left side to the front derailleur and on the right side to the rear derailleur. There is a plastic insert under the bottom bracket that guides the cables. Cables must be bought to match the shifting system used. Ride-on makes special coated cables that run somewhat smoother than regular cables, but don't really justify the price. Normal cables should be oiled with Teflon oil (which doesn't gum up with age) before being inserted into the housing.
Shortening the housing is difficult and requires a special tool, or at least a sharp fine metal saw. The housing should be held by a vise. Saw it off very close to the vise grips, then file the sharp edges and smooth out the inner plastic tube. Use metal caps on the ends. Cables are usually too long; cut them with a sharp cutter and either put a cap on the end or solder the end (but don't use too much solder or they won't fit through the housing caps). Uncapped unsoldered cables fray.
See Also an article on "Chainwheels,Cogs & chains"