Clutches with lots of miles may have notches worn into the splines, which prevent the plates from engaging smoothly, or cracks between the finger webs of the outer drum. If anything significant is found replacement is the only cure. Finally, check the clutch hub nut just to make sure it hasn't loosened up on you. If it has, follow the tightening procedure detailed in your manual.
The photo's not great but you can clearly see the wear marks in the hub and drum. This one's actually in pretty good shape.
Inspection and reassembly
Because the clutch was slipping it's a given that you're going to replace the friction discs, so there's no real need to inspect them. My recommendation is to always replace the clutch springs as well, although if the spring's free length is within factory specifications you can certainly reuse them.
Visually inspect the steel plates for damage. If they're scored, galled or show signs of being overheated (they'll be blued as if put to a torch), toss them. If they look good measure the thickness and compare it to the factory dimension. If the plates are within specification they can be reused provided they're not warped. To check, lay the plate on a flat surface (a heavy piece of glass works fine) and see if it rocks or if a feeler gauge can be slid under any side. Even easier: Place two plates together and pinch them at one point. If they separate they're warped. If they don't, flip one of them over and try again. If they remain flat they're fine and can be reused.
The last step before reassembly is to remove all traces of the old gasket from both sides of the case. This can be tedious, but stay with it-the cleaner the surface the better the new gasket will seat and the less likely it'll be to start leaking down the road.
If the steel plates aren't scored or blue from overheating they can be reused provided they're still within specification.
Installing the new clutch
Clutch plates should never be installed dry; both the frictions and the steels should be given a good dousing in fresh oil beforehand. If you've got time let the friction plates soak for at least half an hour in a pan of clean oil to swell them to their working dimensions.
In most instances a friction disc will be installed first, followed by a steel plate. Before you install the first steel plate rub your finger over the teeth. When the plates are stamped the process leaves one smooth and one sharp edge. Some guys like to face all the sharp edges toward the pressure plate, claiming this gives the clutch a smoother action and prevents premature clutch-hub wear. Some point them toward the inner hub, claiming the exact same thing. I've tried it both ways and never noticed a difference, and as far as I'm concerned, so long as the sharp edges all face the same direction it doesn't matter which way they're pointed.
All-new plates and springs are the way to go.
Once the plates have been put in, oil the throwout bearing and install it, followed by the pressure plate. If your clutch has coil springs install the bolts in a criss-cross pattern and tighten them evenly, using your torque wrench for the final setting.
Wipe down the gasket surfaces of both cases with a solvent-soaked rag to remove all traces of oil. Then apply the gasket sealer according to the manufacturer's instructions and let it air-dry. Hang the gasket on the crankcase side, then slide the cover into place and screw it down. Many a good clutch has been ruined by a sticking clutch cable, so inspect yours and if need be replace it before you consider the job finished. Likewise if your bike uses a hydraulic clutch, now's the time to change the fluid. A new clutch will wear in over the first 500 or so miles, so don't be too concerned if the adjustment goes off slightly during that time. By that same token the bedding-in process will contaminate the oil and filter to some degree, though by how much is debatable, so my advice is to halve the recommended interval to the next oil and filter change.