This is a description of a DIY spectroscope (or more correctly - spectrograph, as I use a camera to record spectra) of my design. The core element is a transmission diffraction grating slide with 1000 lines/mm grating, which can be purchased cheaply online (as cheap as 5$ CAD with shipping, on ebay). The two other critical components are a collimator lens (I used an old SLR Rikoh 50mm f/2.0), and a camera lens + camera. I use a B&W astro camera (which uses the C-mount) ToupCam with a zoom C-mount lens.
All the required equations can be found on this great site:
https://ibsen.com/technology/spectrometer-design-guide/
(the "Transmission grating based spectrometer" part).