When do I use のは/のが?
In some sentences that I've been given, these particles are used and I'm not sure when is the appropriate place to use them. For example, たいそう見るのが好きです uses のが, yet it seems to be there for no apparant reason (at least to me). So, when do I use のは and のが?
の is added to the end of a verb to make it a noun in this case, rather than being part of the particle. So 見るの is the noun form for seeing / watching. You are talking about enjoying the act of watching gymnastics, so the verb becomes a noun. が is required in front of the adjective 好き.
The original poster only used ～が好き as an example. A は B が 好き is a fixed pattern. While りんごが好き doesn't actually use a personal pronoun, it is implied, so it follows the same pattern.
For simple statements, such as 'Teaching Japanese is difficult', you would use normally use は (日本語を教えるのは難しいです）unless you want to stress that teaching is difficult as compared to something else (特に日本語を教えるのが難しいです - Teaching Japanese is especially difficult）.
Determining whether to use は or が is difficult for all Japanese learners. Usually it takes a lot of exposure before becoming more second-nature. That being said, having a clear grasp of the fundamentals never hurts. There are online resources to learn more, including one here
Understanding the difference between は and が would be your first step. In this case が emphasizes that 'Watching gymnastics' is the thing that you like, whereas は would mean that you simply enjoy watching gymnastics. これはいいです。This is okay. //// これがいいです。This one is substantially preferred.
Many others have posted the same inquiry. Recommend to search the discussion boards.
BJCUAl's answer is correct, but I think it gets even more complicated.
I actually had a は vs が conversation with my Japanese friend the other day, in the context of それが分かる vs それは分かる. The former has a particularly dismissive tone, something like, "yeah, I know that (already)" and it seems that the key is that が is "ignoring" the other possible things you can know. So the tone is that of a know it all. However, in the latter case, the は is communicating "I know that one thing, among other things".
I'm no expert on this by any means - Still trying to figure out a way to conceptualize the difference to myself. It would be one thing if it was a simple grammar mismatch, but the fact that it can make you seem like an ass on top of that makes it pretty essential to solve :P