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One of the simplest ways to do it is to just output the stuff you want to save to a file. So you might have something like:

PlayerName
Score
QuestionNumber

Then to load, you just read the...

What about it didn't make sense? You would output whatever you wanted to the file, then you'd read it in however you wanted to do the loading. What things are you trying to save and load?

It's definitely possible, and the terms I gave you to google are the best place to start :)

You could output it to a text file and then read it in (google Java file IO), or you could look into serialization (google Java serialization).