This depends on what type of monthly pass you get. Because North Sheen is in the London “zones”, you can choose to get a travel card or Oyster card, which cover all transport within those London zones, OR you can get a rail monthly pass between two specified stations, which only allows you to do that particular journey and no other.
North Sheen is in London zone 3, so if you got a travel or Oyster card, you’d need one for zones 1-3. It’s a very small station, which only has a train line. Also, if you get trains direct from north Sheen to Waterloo, they will be the slower trains, as the faster ones only stop at a few bigger stations and go straight through the smaller ones. If you’re v close to north Sheen station it’s probably still best to do this, but do look to see if you can more easily get to Richmond or Barnes or somewhere if that gives you more flexibility. (Note that if you wanted to go to Richmond, that’s zone 4 so you’d need a zone 1-4 pass).
As a student you can get cheaper fares but you need to plan in advance with photo card etc.
https://content.tfl.gov.uk/18-plus-student-oyster-photocard-fares.pdf
Here’s a map of the zones and what station is where (click on view map) https://tfl.gov.uk/maps/track
The monthly season train tickets that just would literally allow you to go from north Sheen to Waterloo and back don’t allow student discount https://www.southwesternrailway.com/train-tickets/season-tickets/monthly-train-tickets
I think this is still cheaper than getting the oyster monthly pass, but it is more restrictive- you may find it is really worth having a zone 1-3 or 1-4 pass, as this will allow you to get any tubes or buses or other train journeys within this zone all included. It all depends on what you’re likely to be doing.
For all of these, you’d have your monthly pass and treat it as your ticket - swipe in and out with it each time you make your journey.