Most systematic way would, probably, be to work through one of the canonical textbooks for cosmology (e.g. Dodelson, Peacock, Coles, Liddle and Lyth, Mukhanov, and so on).
One of the problems with cosmology is that it quite often invokes a range of disciplines from physicss. In a very general sense, expect to be comfortable with:
- General Relativity (e.g. FLRW models are the standard model, cosmological perturbation theory)
- Statistical Mechanics/Thermodynamics (used in early Universe nucleosynthesis etc)
- Quantum Field Thoery (if you're interested in inflationary cosmology etc)
- Statistical methods (models for the Universe from inflationary cosmology are statistical in nature and you should be comfortable in using statistical tools to describe these models)
- Electrodynamics/Radiative Processes (tending more towards the astrophysics side of things but still an important process to understand given that most information of the Universe is currently retrieved from radiative processes e.g. CMB, Supernovae, 21cm, observations of Galaxies etc).
- Quantum Mechanics (a prelude to QFT but also required for a lot of modern physics).
It would also help to have an understanding of the basics of astrophysics and stellar/galactic physics etc. If you've just started self-learning physics then you should hope to get a basic understanding of all the core subjects (Electromagnetism, Classical Mechanics, Quantum Mechanics, Statistical Mechanics, General Relativity, Quantum Field Theory - if you're interested in the theory aspects, Stellar Physics, Galactic Physics) before working through most modern cosmology, you can always fill in the blanks along the way. Sorry if this is not helpful, it's never easy to judge the level that you're currently at or what level you hope to work towards. Have fun though :)