Functional Grammar involves considering grammar from the point of view of the USE of the language, this is, language operating in context. Learning Traditional Grammar, as you have experienced, does not necessarily mean you learn how to use the language in actual (=real) communication. So now we teachers and learners are trying to understand, teach and learn using FG.
In our Functional Grammar section not all is technically speaking FG, but I'll be trying to turn it all into that!
The first thing we've got to do is change our approach: literal translation is not helpful. It's more helpful to know what our communicative aim is in terms of the message we want to create. Use your intuition: what do we want to communicate who to, where, how...? What do you wish to do in a situation to somebody! Here is a little chart that can help you learn about Language Functions and Modals (1 page). If you analyze it you will see that thinking in terms of Language Functions (what we can do with language) is going to help you use Modals better than thinking in terms of (inaccurate, misleading) equivalences (literal translation) such as "have to" is "tener que" and "must" to "deber"!!. Oh my! That's terrible! To learn how to use the modals, you need to consider apart form the modal itself, the subject and the type of sentence: affirmative statement, negative statement, affirmative question, negative questions... I tried to create a table following this idea, focused on "can", but I need to improve it. Have a look (1 page).
Are you getting the feeling of what I mean?
Let me explain further by using an example... If you want to translate ¿Qué me pongo? and you use literal translation, the result will be completely disastrous. But if you ask yourself, "Which is the language function I'm using?", which is my communicative aim and intention?, you'll get a clear answer: you want to ask for advice, you want to be polite. In English there is a modal auxiliary verb to ask for advice: should. So the functional translation of that sentence is: What should I wear? The different translations we may get of a same sentence depend often on our communicative aim, on the function we want language to perform for us, and on context (the situation, the people involved), of course.
Another example. If you want to make a proposal, you have different language items to do so: you can use "Let's do (whatever)!" (enthusiastic proposal, includes yourself), "Why don't we (whatever)?" (less pressing because you make your proposal with a question), like "Would you like to (whatever)?" (addresses the listener, polite), "How about (whatever)-ing?" (no "person" mentioned -- but it includes all -- so it's more indirect or neutral), "We can/could (whatever)" (expressing possibilities we can choose), "I want to / I'm dying to (whatever)" (you are really close to the listener to be so blunt!), etc.
Browse your textbooks, the table of contents, to find the names of different language functions, e.g. Asking for information, and then list chunks of language that help you meet that language function. On Talking People, we are developing this in the section called "Useful Language", which offers us the material to create some "Useful Language" episodes on the Talking People Podcast, too. Check it out!
Also, check out the FAQ webpage on English - Teaching/Learning
The segment "Useful Language" on the Talking People Podcast (use the Category "Useful Language" -- on the right-hand column -- to get a list of these episodes)