Do the language exchange. (How do you expect to learn Chinese if not by chatting with Chinese speakers?)
My personal opinion on grammar (and pronunciation etc.) is that you’ll probably be most successful learning it from use. Pointedly studying grammar (as much as you may, like me, enjoy it and find it useful) has always seemed to me like trying to take a short-cut into the language. I think you can improve your Mandarin by taking this short-cut, but since the short-cut is rougher and steeper as well as quicker, you’ve got to be a bit careful about how you hike it.
(1) Memorizing grammatical formulae is probably not a good idea. Any decent mathematician or logician will tell you that memorizing formulae, theorems, and whatnot, while this may be useful, is far less so than developing the ability to see and create patterns within the system or language you’re working with. How do you develop this ability? Exposure to the language. Playing with the formulae and theorems others give you. Looking at good examples and analyses without getting stuck at the level of only decoding and reencoding Chinese grammar but not actualy playing with it day-to-day.
A good step in this direction is the book Mandarin Chinese: A Functional Reference Grammar by Charles N. Li and Sandra A. Thompson. Lots of good examples and straightforward explanations.
(2) Pay attention to the grammar points that matter: those that are significantly different from what you’re used to. Of the ‘ba’ construction that you posted, the better part of the construction is not so structurally different from English. Take John’s example.
Wo xiang ba keben cha dao ta houlong limian
(I would-like OBJ-text shove arrive his/her throat inside)
I would like to shove the text into his throat
From the perspective of an English speaker, only two elements of this sentence obviously beg for analysis. Focus on these and leave the rest until you bump into a particular difficulty.
(1) The object marker ‘ba’
Using ‘ba’ allows you to draw attention to the object and mark it out as particular. Rather than writing
Wo xiang cha keben dao ta houlong limian
I would like to shove a text into his throat
you indicate a specific textbook (one that is being, or could be, grabbed; ‘ba’ means something like ‘to grab’) by using ‘ba’.
Wo xiang ba keben cha dao ta houlong limian
I would like to shove this text into his throat
The workings of this piece of grammar are simple. You move the object of a verb out from behind the verb and place it in front the the verb, adding ‘ba’. The meaning, if not apparent above, can be illustrated by a similar construction in English.
I would like to take this text and shove it into his throat
In fact, ‘ba’ originally meant something not so much different from ‘take’, and the Chinese word for take, ‘na’, can also be used in the same way as ‘ba’.
Prepositional phrases in English take the form of a preposition followed by a noun phrase. Hence ‘onto the table’, ‘into his throat’, ‘under the bridge’. In Chinese, one uses ‘dao’ (arrive, to) or ‘zai’ (exists) followed by a noun or noun phrase followed by a position word. Hence ‘dao zhuozi shang’ (onto the table), ‘dao ta houlong limian’ (into his throat), ‘zai daqiao xiamian’ (under the bridge).
You don’t need to have studied Chinese grammar previously to figure these patterns out. Seeing a few Chinese sentences translated into a language you know well ought to give you enough information to puzzle out what’s going on, and this puzzling out on your own may well wok better than memorizing and trying to reproduce certain patterns. By all means, take a look at the patterns, write example sentences. Just don’t get hung up on them to the point where learning Chinese isn’t fun anymore. And if you bump into a particular piece of grammar that you can’t wrap your head around, ignore it for a while, concentrate on things that do make sense, and then return to it when your Chinese is a bit better. If your Chinese teacher doesn’t like this jumping about or can’t find a way to teach the language to your needs, find a new teacher or supplment that teacher with an effective language exchange partner.
Finally, for fun, see if you can spot the pattern in this sentence.
Qing ni xian tiao zai zhuozi shang, zai zai zhuozi shang tiao.
Please first jump onto the desk and then jump on top of the desk.