Both words have many uses, but what mainly causes problems for Spanish speakers when they both translations of 'como', particularly when they're followed by a noun - for example, the difference between 'like a tourist' and 'as a tourist'.
It will help you understand the difference if you remember that 'like' means 'similar to'. For example:
A crocodile is like an alligator.
A clementine is like an orange.
These two animals and fruits are not the same, but they are similar, so we use 'like' - it's a comparison.
'As' means 'in the role of' or 'in the capacity of'. For example:
He works as an architect
This means that he really IS an architect - that is his job. So if you compare these two sentences -
They worked as slaves.
They worked like slaves.
- the difference should be clear.
In the first, the people really were slaves - this might be a line from a history book. In the second, this is just an idiomatic use, a figure of speech or an exaggeration, just meaning that they worked very hard.
If you are walking round your own city with a friend and he is taking lots of photos, you could say that he is 'like a tourist'. He isn't really a tourist - he is just similar to one. However, you might say that someone from your country went to the USA 'as a tourist' - this means that this was his status on his visa i.e. the capacity in which he visited the country.
Or in a language context, you might begin a sentence 'As a native speaker,....' meaning that you really are a native speaker of that language.
Or if you aren't a native speaker of that language but you speak it so well that people imagine that it's your mother tongue, you might say 'I speak it like a native speaker'.
I hope that helps.