One of the most common questions I get asked is 'How many words do I need to learn?'. The answer is of course to learn any many as you can, but I can be more precise.

Some words are very common while others are rarely ever seen. This means that you can understand a large part of mosts texts with only a limited number of words. How many exactly is a question that you can answer with a lexemic frequency dictionary. These dictionaries are made by taking an extremely large corpus of texts (books, newspapers, etc...), grouping each words by lexemes and listing how many times they came up in the corpus. A lexeme is a 'unique' word that does not depend on conjugation or plurals or declensions. For instance the lexeme 'to be' would cover 'am, is, are, were' etc...

These lexemic frequency dictionaries were made during the Cold War for the purpose of computerized automatic surveillance of other countries - especially Russia.

I have one such dictionary in digital format for Russian. With the files I was able to create a graph of frequency versus rank:

 

The result is that:
the    75 most common words make up 40% of occurences
the   200 most common words make up 50% of occurences
the   524 most common words make up 60% of occurences
the 1257 most common words make up 70% of occurences
the 2925 most common words make up 80% of occurences
the 7444 most common words make up 90% of occurences
the 13374 most common words make up 95% of occurences
the 25508 most common words make up 99% of occurences

This shows clearly that vocabulary frequency follows both the law of Pareto (80% of occurences by only 20% of words) and the law of diminishing returns.

So yes you can probably read any text with only 3000 or 5000 words, but you will always miss some key words. You can't really say that all you need is 3000 words although this certainly gets you to a more or less autonomous stage in your learning, from which you can learn many words by their context.

Lexemic dictionaries also exist for other languages but are hard to find. Non-lexemic frequency dictionaries are useless as they would list you every single variation of words. They are not usable by a language learner.

You can use such a dictionary (with the words and the frequency) to discover new, frequent words which you can learn, or to estimate the size of your vocabulary.