Learning more words is generally a better way of boosting your comprehension than actively studying grammar, since grammar can more easily be understood through context.
For a language like English, the number of words you’d need to be fluent is over 10,000. Increasing your vocabulary is therefore always a useful task, so if you don’t know what to actively study, try to do that. While 10,000 is a large number, you will get there eventually by chipping away at it every day.
Don’t learn related words together
Although it might seem like a good idea, it’s best not to learn words together if they are in any way related.
This is because the similarities can cause you to confuse them. This includes near synonyms (rely/depend), opposites (fast/slow), and words typically recounted together (days of the week, numbers).
Word lists
It can be helpful to keep a list of those words you have looked up and find interesting enough to want to remember. This can serve as a useful reference, and the act of writing a list by hand can aid memorisation.
Word lists should not simply be read over but revised with one side covered to get your memory working.
Advice on learning vocabulary
Other than by flashcards and dictionary lookups, the way you learn words is by encountering them naturally and deriving meaning through context and repetition, as you have done with your native language.
This takes a lot of input and can sometimes be imperceptible but is highly effective. Any advanced learner will tell you a large portion of the words they know came to them this way.
Mnemonics
Mnemonics are a general tool that turn vocabulary into easy-to-recall mental images that serve to help you remember a word.
Mnemonics can be very useful to learn vocabulary quickly, however the word won’t be truly learned until you don’t need the mnemonic and can use and understand the word automatically. Mnemonics are a useful tool to improve your recall, not an easy way out of having to absorb the language.
The most common method is the keyword method.
This links the word you want to learn to a similar-sounding word in your native language. For example: Imagine you want to learn the French word for “car”, which is “voiture”. You might note that the word “voiture” sounds like “vulture” in English.
You can mentally link the two by imagining a car with a vulture on top of it, or if you are very imaginative, imagine someone built a car shaped like a vulture. Now when you want to talk about a car, you’ll remember the vulture on top and that the French word sounds like “vulture”.
The more vivid, bizarre, or surprising your mnemonics are, the more effective they will be. You will be surprised by how well they work.
