When you do something in a hesitant, uncertain way, you act falteringly. If your math teacher asks you the answer to a problem you don't understand, you'll answer falteringly.
When you're just learning a new language, you're bound to speak falteringly for a while, not confident in your ability to find the right word, and a little tentative about saying the wrong thing. People move falteringly too, the way you step falteringly into a dark room, feeling around for furniture so you won't walk into it. This adverb comes from falter, meaning "hesitate," which originally meant "to stagger or totter."