What are the conventional ways by which the speed of a polyphase induction motor can be changed?

You use the term "Polyphase" Induction motor ?? As% of all industrial motors are polyphase (they would be, its just a term for the multiple windings per pole) then the use of the term interests me.

In answer to the question there would be two very obvious methods of acheiving speed change.

1. A gearbox

2. A VSD or VFD (depending on where you are we use both terms)

It completely depends on the need to change the motor / shaft speed, the application for which this is a requirement.

In case of single phase electric motors , it is known that decreasing the number of poles will increase the speed , on the other hand also increasing the frequency will also increase the speed as well where there is a formula that adapts the process .Now if varying the frequencies is not bringing out your required result , you may use a gear box .

In case of three phase induction motors , it depends on the types:

1-Wound rotor three phase induction motors , where in this case you can adapt the rotor speed limiting the voltage to the wound rotor my means of inserting resistances in series , this will work on limiting the strength of the magnetic field and reduce the rotor's speed .

You can also use frequency convertors and mechanical options.

2-Squirrel cage three phase induction  , similar to single phase.

1)By changing the poles.

2)By changing the slip.

3)By varing the frequency.

Now the third one is adopted all over world,also the simplest method,by installing one vfd,the squrril cage induction motor speed can be varying any speed to the name plate speed.