I use Schaller tuners, and have been using them for over 17 years.  There are better (and more expensive) tuners on the market, but I like the Schallers because they are not expensive, I can get them locally, and the plastic knobs are easy to replace with wooden knobs.  When first installed they can be a bit stiff, but after a couple of years will wear in and work smoothly.  I have used Waverlies which are very nice and silky smooth to tune, but at more than 5 times the price they are not a standard option on my mandolins.  The Schallers do stay in tune, I can play a whole gig without needing to re-tune but they are not smooth as the Waverlies.  This is how I make the wooden tuning knobs and install the tuners.
Remove the knobs
Firstly remove those horrible plastic knobs the tuners come with.  They can be removed by crushing the plastic with fret nippers or by heating them in boiling water.  I use the nippers because it is safer, no burned fingers.

Remove the glue
Next step is to remove the old glue from the tuner knobs.

Cut the Gidgee
This mandolin is going to have Gidgee tuning knobs.  Gidgee is a very hard and dark reddish brown coloured wood from an Acacia tree that grows in arid regions of Australia.  It is often used as an Ebony substitute in Australia.   A slice of Gidgee is cut on the bandsaw.

Gidge sliced
Here it is after cutting.  This wood is so hard that it is not unusual for the bandsaw blade to break while cutting, and after a few slices like this the blade is not useful for much else.

Plug cutter
Cut the tuning knobs from the Gidgee slice with a plug cutter on the drill press.

Remove the plug of wood
Pop it out of the plug cutter with a screwdriver.

Drill the hole
Now drill the hole.  This is a two stage process so the knob fits firm on the shaft, but not too tight so it splits the wood.

Bunch of plugs
I usually do a batch of plugs at a time, enough for a few mandolins.

Thickness the knob
Now start shaping the plug into a knob on the linisher.  Firstly sand it flat to the right thickness.

Rough sand the edge
Rough sand the edges.

Rough shape
Rough shape the face of the knob.

Fine sand
Fine sand the edges and the face of the knob.

Fine sand the corners
Fine sand the corners.

Extra fine sand edge
Extra fine sand the edges.

Fine sand the faces
Extra fine sand the face.

Knobs finished
Here are the knobs finished with an Ebony knob for comparison.

Dry fit the knobs
Dry fit the knobs to make sure everything fits.

Apply glue
Apply high strength epoxy glue.

Push on knobs
And press the knobs onto the shafts.

Wait to cure
Here they are all fitted and now we need to wait at least 25hrs for the epoxy glue to cure.

Oil the knobs
After the glue has cured the knobs are oiled.  I use olive oil, which gives a nice flat finish, but any finishing oil can be used.  Here the front set has been oiled.

Ream the holes
Now is time to install the tuners.  Firstly ream the tuner holes to remove excess finish.

Push on bushings
Press in the bushings.

Push in bushings with drill press
Press the bushings down tight with the drill press.

Drill holes for screws
Insert the tuners and drill the screw holes with the drill press.

Screw in the screws
Screw in the screws.

Tighten cog screws
Make sure the cog screws are tight, but not too tight.

After all the handling often much of the manufacturer's lubrication gets wiped off so I usually add a small drop of light machine oil.  It doesn't take much.

Wipe off excess oil
Mop up any excess oil.

Now check the tuners work smoothly, and we are finished.  If not, a bit of fiddling with the various screws usually fixes the problem.