Loanwords get their own post, because there are so many of them. Remember how many languages in a particular region are often related, with much of their vocabulary either shared or semi-transparently related? Languages also have a strong tendency to “borrow” vocabulary from other (even completely unrelated) languages that they are in contact with, further reducing the amount of novel vocabulary to be learned from scratch in many new languages. Converting between the form of a word in one language and the borrowed form in another language is often simply a matter of applying a formula, and can sometimes be done on the fly in a pinch.
This is, of course, not a perfect solution, but nothing here is. You will still encounter numerous false friends, and sometimes the formula to get from one form of a word to another will be less obvious than it could be — a good dictionary is still an essential tool when starting a new language, and you shouldn’t rely solely on your instincts to determine a word’s meaning, even if you are a linguist yourself. But in a pinch, reaching for an international word that might have been borrowed into your target language in some form can be a solution if you aren’t sure how to say something.
Note that a lot, although not all, of the international vocabulary discussed in the previous post falls into the loanword category. Many of the traits of loanwords can also be applied to cognates and other types of international vocabulary, and many of the “international” words that you will come to recognize became international by being borrowed from one language into another over a relatively short period of time. This is especially true with scientific terminology, which is often coined in a particular language — often English nowadays — and then exported whole cloth or as a calque to other languages. It can also pay to keep your eyes open for familiar brand names that may have become genericized in your target language, even if the original generic word would have been unfamiliar.
At a broader level, though: regardless of what anyone may tell you, linguistics and language learning are not unrelated, even though they are not simply two branches of the same field. Linguistics, and especially historical linguistics, is an incredibly useful tool when studying a foreign language, and even a little bit helps. One purpose of these posts is to teach a tiny bit of basic linguistics to language learners, in the hope that it will make their lives easier.
Now, a word of warning before you go out and assume that every familiar-looking word is a loanword with a familiar meaning: so-called “false friends” are very real, and words that resemble one another may have different meanings, even if they are ultimately related. For instance, the French verb demander is related to the English verb demand, but the former simply means ‘ask’. However, as the example reveals, you can often find at least some connection between the meanings of related false friends (i.e. demanding is arguably just a more forceful form of asking), so don’t discount etymology!
And one last thought: you should be looking not just at words borrowed into your target language from languages you already know, but also the converse — words in languages you already know that originated in your target language. Think about all of the French vocabulary that has made its way into English (often with a somewhat altered meaning) — if you dig deep enough, learning about those words will make learning French vocabulary much easier.