Syntax : how they assemble words

Syntax is the way speaker of a given language arrange words so that they make meaningful phrases. Grammar is a set of rule that tries to explain you how they do this. Keep in mind that the ultimate reference for "correcteness" of speech is the speech of a person from the social group you want to speak to, commonly the speech of the educated upper class.
Difficulty of learning syntax depends a lot on the closeness of your target language to the ones you already know. Some languages have a lot in common in this regard, like the latin languages spanish, french, italian, portuguese, etc... where you can translate word-by-word and get it right. Others, like german, have pretty strange ways of building phrases like "The yesterday-talken-about airplane is today morning found become" that take some time to master. My advice is to read a lot (sample phrases in good grammmar books or newspapers) and then let the "rules" be infered naturally by your mind. Learning rules in the grammar book and then trying to apply them to new phrases does not work. Rather, you should find good drills, preferably on audio tapes, and practice them over and over again. If you must think before your speak, you will never be fluent.