It is very easy to transpose glasses or spectacle prescriptions. You need to follow some basic rules to transpose minus cylinder to plus cylinder or plus cylinder to minus cylinder form.

Rule 1: To add spherical power and cylindrical power and you will get new spherical power.

Rule 2: Change the sign of the cylinder (minus to plus or plus to minus) without changing cylindrical power value.

Rule 3: Change the cylinder axis 90 degrees apart ( if you have axis 10 to 90 then add 90 and 100 to 180 then subtract 90). You will get a new axis after adding or subtracting.

Example 1: Sph +2.50 D / Cyl -1.50 D Axis 170

Adding Sph +2.50 D and Cyl-1.50 D = New Sph +1.00 D

So, here +1.00 D is new spherical power.
 
Changing the sign of cylinder minus to plus. So, new cylindrical power would be +1.50.

Lastly changing the axis 90 degrees apart. So, in this example axis is more than 90, you need to subtract 90 from 170. So, new axis would be 80.

After Transposition:
Sph +1.00 D / Cyl +1.50 D Axis 80.
 
Example 2: Sph -1.75 D / Cyl -1.25 D Axis 60

Adding Sph -1.75 D and Cyl -1.25 D = New Sph -3.00 D.

So, here -3.00 D is new spherical power.

Changing the sign of cylinder minus to plus. So, new cylindrical power would be +1.25.

Lastly changing the axis 90 degrees apart. So, in this example axis is less than 90, you need to add 90 to 60. So, new axis would be 150.

After Transposition:
Sph -3.00 D / Cyl +1.25 D Axis 150.
 
Example 3: Sph +1.75 D / Cyl -3.25 D Axis 40

Adding Sph +1.75 D and Cyl -3.25 D = New Sph -1.50 D.

So, here -1.50 D is new spherical power.

Changing the sign of cylinder minus to plus. So, new cylindrical power would be +3.25.

Lastly changing the axis 90 degrees apart. So, in this example axis is less than 90, you need to add 90 to 40. So, new axis would be 130.

After Transposition:
Sph -1.50 D / Cyl +3.25 D Axis 130.
 
Example 4: Sph +0.75 D / Cyl +1.25 D Axis 110

Adding Sph +0.75 D and Cyl +1.25 D = New Sph +2.00 D.

So, here +2.00 D is new spherical power.

Changing the sign of cylinder plus to minus. So, new cylindrical power would be -1.25.

Lastly changing the axis 90 degrees apart. So, in this example axis is more than 90, you need to subtract 90 from 110. So, new axis would be 20.

After Transposition:
Sph +2.00 D / Cyl -1.25 D Axis 20. 

You should know about Refractive diagnosis also.