I seem to have been much more successful than the median student in my Français classes. Accordingly, I try here to distill and share my methods of success.
I may err in interpreting how effective my methods are, and may have included some actions here which don't actually help. Beyond that, different things work for different people; what helps me might not help you. Your mileage may vary.
Some of these methods rely on exploitable attributes of Français in particular. Some are more general, and can help with any language learning. Some can apply to any subject of study, not just language.
Suggestions here may seem obvious, often sith they are obvious. I preferred to err on the side of going over too much of what people already know, rather than skipping over important basics.
Some students seem paralysingly ignorant of Français grammar, not knowing how to structure a sentence or a part therein, and getting stuck on that. There's a straightforward way to avoid this issue. If you don't know the grammar to express something in Français, guess by directly translating the corresponding structure in English. Alter phrases in that translated structure as you know appropriate. English and Français are more similar than you might expect. This won't always be right, but in many cases, it will be, and it lets you move on to other concerns.
For example, you might want to express (as I did) that which, in English, is: "The brother was stronger than the main character, sith he had genetic modifications." Translating parts of that sentence, in order: "the brother" to « le frère », "was" to « était », "stronger than" to « plus fort que », "the main character" to « le personnage principal », "sith" to « parce que », "he had" to « il avait », "genetic modifications" to « augmentations génétiques ». Combining them, we get « Le frère était plus fort que le personnage principal parce qu'il avait des augmentations génétiques », which almost perfectly agrees with a machine translator, despite how directly I inferred it from the English.
But as I said, this isn't always right. It's just a weirdly effective starting point. Hopefully you will be taught about — and remember to apply — the cases wherein Français grammar diverges from English's.
Besides grammar, Français and English share a lot of words (i.e. cognates). Perhaps a quarter of English words come from Français.
If you see an unfamiliar word in Français, but it resembles an English word, you may guess its meaning to be similar to that English word. E.g. I didn't know « indiquez » (as in « Indiquez le genre »), but it looks like a verb, and like English "indicate", which fits the context. So I interpret the phrase as "indicate the genre". Wiktionary confirms the words to be cognates.
This also works in the other direction. Many English words — especially uncommon, longer ones — have straightforward cognates in Français. You might then translate the word by changing its spelling to fit Français (by a set of rules picked up by experience). I used « génétiques » earlier, but I never studied that word — I inferred it on-the-spot from English's "genetic".
As with grammar, this isn't perfectly reliable, just a good starting point. Sometimes words that look like cognates aren't, like « blesser » and "bless". Sometimes words that are cognates have meanings that diverged, like « journée » and "journey".
To get the most out of this profusion of cognates, study etymology: the history of words. Among the most important lessons applicable here are that the most basic words in English come from Germanic, whilst many more elaborate words come from Français, Latin, or Greek, the first of which gets most of its words from Latin. Latin is also the basis of many other languages (notably including Español).
There are patterns in the structures of words from various languages. For example, words containing "ct", such as "spectrum", are almost always from Latin, and thus have cognates in Français, such as « spectre ». Words with "ch", such as "hierarchy", pronounced as /k/ are almost always from Greek, sometimes thru Latin, and thus may have Français cognates, such as « hiérarchie ». Words with "ck", such as "stack", are almost always Germanic, and as such have no Français cognates. Français adds circumflexes to vowels, as in « l'hôpital », in words which tend to have "s" after the vowel in cognates in other languages, as in English's "hospital".
You can learn more etymology by looking up words in dictionaries which include etymology. I use Wiktionary.
You can get many words to look up by reading Français text — as would probably be assigned in a course, and it helps to find some outside of class. (There's more to be gained than vocabulary by reading enjoyable text in the language you're learning.) Look up words that you don't know, aren't apparent cognates, and are important to understand the text. You get even more words, perhaps too many, if you relax any of those conditions.
How to remember those words? The same way you should remember essentially all studied knowledge: spaced repetition, with active recall and interleaving. Many others have already explained spaced repetition — such as Bjornstad, Kirsanov, and Wozniak — so I just mention it here. See other sources for the details.
It is from that method that "studying for tests" seems absurd to me. I do not study for tests. I study for life — spread out over time — and tests are part of life, so I happen to have learned much of the material at the time of the test.
However you study, remembering gets much harder if you never bother to understand what you study. Make sure to actually understand the Français, rather than blindly grammar-stacking! It helps for such understanding — and for practical fluency — to deeply study and retain the basics that so many students seem to forget, like the present-tense conjugations of « avoir » and that it translates to English "to have".