Nasal vowels are produced by forcing air through both your mouth and nose simultaneously. We have such vowel sounds occasionally in some English dialects, but they aren't considered significant (that is, if they are said non-nasally, they are not misunderstood), which is why most IPA transcriptions don't include the /◌̃/ nasal sign.
One example is to compare the vowel sound in the word and to add. The word and has a nasal quality that add does not (at least in General American). But in American, this always happens before certain consonants (typically m and n). In French, Portuguese, and other languages, these sounds will happen in other parts of the word, which makes them seem difficult for native English speakers.
One technique that can be used to nasalify (is that a word?) a vowel is, to practice it in conjunction with an /n/ or /m/. In fact, in Portuguese, the nasal vowels are often even spelled this way (and I suppose probably evolved this way). I suggest focusing your practice on /m/, because it is more nasal than /n/ for the simple fact that your lips are closed, so the sound you produce with /m/ is purely nasal, no matter what.
As an example, to practice the /ɛ̃/ sound (French inde), find a familiar word (I'll use English examples, but if you're a native speaker of some other language, substitute your own) with the same vowel sound--ideally at the beginning of the word, because that's easier to isolate. I'll use the English word egg, pronounced, of course /ɛɡ/. So now you know how to say the non-nasal /ɛ/. Now add an m to the end. Practice /ɛm/. That sound you make between the beginning of your /ɛ/ and the beginning of your /m/ should now be the nasal /ɛ̃/.
Of course, vowel sounds (even the non-nasal varieties) vary between languages, so your nasal English /ɛ̃/ may not be the same as a French nasal /ɛ̃/ (and of course an English non-nasal /ɛ/ is not the same as a French non-nasal /ɛ/, either!). So this absolutely will not substitute for listening and speaking practice with a native French speaker.
But it can be a strong step in the right direction toward nasalizing your vowels.