Glantri's Island
"Hmmm, well a lot of the systems got rules out do to requirements or reliance on physical objects which I wouldn't have access to right now. Just thinking out loud to list them, but Alloymancy from the mistborn trilogy involves injesting and burning precise metal compounds, which each have different effects, from being able to push or pull on other metals to soothing or rioting emotions and so on. But I don't have those metals, and the limitations are fairly strict to what they can do. Ferochemy from the same series allows one to store ones attributes in those metals while wearing them and call on them later. That will be useful, especially being able to store weight or increase weight using my previously stored amonut, but I would need to find an iron bracelet or other piece of iron to use, my sword is steel which is used to store steel. But once again, very limited in applications, even if some are incredibly useful.
Past that there are a number that use incantations and spellbooks, often assisted with wands or staffs, from Dungeons and Dragons wizards to the wizards in the Dresden files to Harry Potter, but none of those sources really go into HOW things are done, just that they are. I suppose I may remember some key words from individual books, but not most that's for sure.
Then there's the stormlight archive, which I remember a lot about the magic system, it's actually based on following the ideals of your order. But I only know 3 of the ideals of one order. Not to mention it's based on absorbing stormlight, a phenomenon of Roshar that has tremendous storms of lightning and wind and also stormlight. The system is rather impossible to use outside of that. Perhaps that's one of the problems, I like books where the magic has a lot of limitations on it's use, it makes for a more interesting read. Perhaps video games are a better source for my first type of magic and then move on to these others at another time, or wait until I land in a world that has a similar type and learn from people who know it?
On the topic of video games, the system I know best would be Final Fantasy's materia system. The general concept is that magic is channeling the life essence of the world, which when concentrated highly enough forms beads of materia. It would probably be easiest if I had one of those beads, but I can probably try something small and slow without one. Perhaps just a basic wind spell to summon up a gust, just to see if I can get it working tapping into this worlds power."