"I can see her."
Depends on what you precisely mean by important. For meaning it virtually never affects the understanding, with a few exceptions. For stylistic purposes, it is pretty important, which is why you have native speakers constantly disagreeing on this forum about whether given word order is natural or not. ;-) Generally, you emphasise different parts of the sentence by changing word order, so certain specific order might have "unintended consequences", but I would say you don't really have to pay attention to that, until level B2/C1 in language competence.
That said, there are a few things you should pay attention to:
Do not separate "nie" from verb – "nie" is very flexible and can go with almost every part of speech negating it and on top of that, Polish has normal negations, double negations, triple negations and something that(in my opinion) could be most aptly described as "sentence-wide negation agreement"… All that means that when you separate "nie" from verb, you will negate something else and the complicated way Polish negations are parsed will mean that most of the times the meaning of the sentence will go completely astray.
Do not separate "się" from verb – in Polish it sometimes happen that reflexive pronoun is separated from the verb by other words, but staying on the safe side and putting it right after verb(unless it would end up at the end of the sentence, then right before verb) is never really wrong.
Use always stressed versions of pronouns at the beginning of the sentence – not much to add here, it is a rule in Polish, otherwise the sentence is just ungrammatical.
Avoid (unstressed especially) pronouns at the end of sentence – apparently we try not to do it in Polish
Remember that adjective before noun describes particular trait of the noun while after noun it describes wide category/class to which noun belongs – this is important, because it is the rare case where the meaning is changed by word order.
That's pretty much it – there are a lot of other rules in Polish and many intricacies of word order, but – again – most of them don't really matter until you get a good grip of the basics and if you follow these rules I just described, while you might create some sentences that might sound somehow unnatural, you should never construct a grammatically wrong sentence(unless I forgot about some rules – that is possible, as a native I never really consider those when I construct sentences ;-) ).
Emwue is right , but there are three things that I would add:
nie is always before verb.
preposition is always followed by (adjectives) noun/pronoun.
(what are you talking about= O czym mówisz)
the safest bet is SVO word order, you just have to make sure pronoun or się does not stay at the end
As for the position of "się" - it is better not to put it at the end, but it is strictly forbidden to put it as the first word, therefore in short orders and instructions in which reflexive verb is used, "się" has to go to the end, eg.: "Rozbierz się!", "Umyj się!", "Uspokój się", "Oprzyj się".