These two words have similar meanings but DIFFERENT USES. What the previous members have said is true, but please don't think that these words are interchangeable.
1. 'Way' is a very common word in English. The 'way' usually explains HOW you do something. ( In French: la manière, la façon, le moyen)
What's the best way to learn Spanish?
I like the way that you dance.
My teacher explains things in a very clear way
'Way' can also mean a route, in the sense of how to get somewhere:
Can you tell me the way to the station?
You CAN'T use 'path' for any of the above situations.
2. 'Path' usually refers to a physical thing ( 'un sentier'. 'un chemin') .It's like a road, but it's very narrow, and you walk along it.
There is a narrow path through the forest
We walked down a path to the beach
It wouldn't be normal to use 'way' in these situations - a 'way' is not a 'concrete' thing.
Sometimes 'path' is used in a figurative sense:
eg the path to glory, the path to success, the path to maturity.
These are quite 'literary' in tone, and not especially common.
I hope that this answers your question. Remember - we do use these words differently. If you're still not quite sure, why not give me a few examples of your own of how to use 'way' and 'path', and we can tell you if you are right or not?