There are different opinions on the meaningfulness of testing of private methods, e.g., here and here. I personally think it makes sense, the question is how to do it properly.
I'll answer the "In general" question :-) It only takes a few lines of code to make a method accessible via reflection and there are quite a number of libraries, utils, APIs etc that provide methods for doing so. There's also probably many different techniques you could use in your own code. For example bytecode manipulation, reflection, class extensions, etc. But I'd be inclined to keep things simple. Whilst it can be useful to test private methods, it's also likely that you will only want to test a few. So engineering something complex is probably overkill. I'd just use an established API, or write a quick method to access the private methods I was interested in and let it be done at that.