Clearance means the distance between mechanical parts.
I.e. in this gearbox the between rotating parts in thousands of an inch.
A real gap is positive and a clearance, a pre-load is negative and clamps the parts together. I note that they just give a pre-load with no negative in the tables.
I don’t know which transmission is yours so I just read the first one.
Ok in Vol 2, MT -14 shows the main shaft, part numbers 30 and 31 provide the clearance adjustment or preload.
MT-22 shows checking the gear clearances on the main shaft. Useless you feel you must do this, I would leave this, and it will be close, till the second gearbox when you have the car running. It also shows a press to remove the main shaft bearings.
I think you can check the synro wear clearance with the shaft assembled, they do it when the main shaft is dismantled, if in spec and you have no complaints, leave them. MT-24
MT-26 and MT-27 press on main bearings.
MT-31 press in outer race front mainshaft bearing
Adjust mainshaft main bearing pre-load MT-33 shim table MT-102 p161
Note the main bearing cover enables you to change the adjustment shim from outside.
The next type of transmission has a shim on the shaft between the bearing and the shaft land. MT-55
About all the pressing and pulling. I have used three leg pullers on things like this, if you can get a bearing puller holder like as shown in the manual and use a puller on that it would be better.
To re-assemble you can use a hammer, use blocks and things like sockets to position and drive things in and on.
Be careful not to chip anything, I chipped a Jaguar mainshaft once.
If in doubt it would be better to take in to a machine shop or auto shop and have them do the pressing and pulling. Here in Dallas things like this were about $6-10 a piece. No idea on prices these days.
Take everything at one time, saves set up time. ie get your new bearings first.
(Replace the oil seals.)
(get part number of bearing and go to a bearing supply house. On ball race types the last letter often means clearance, you can use tighter clearance bearings. Automotive often uses "c" clearance bearings loose fit ball bearings.)
Good Luck......