Short answer: the fastest way to sound natural is shadowing: repeating a recording half a beat behind it, copying rhythm and pitch as well as words. Combine it with a small set of fillers (えーと, あのう) that give you time to think, and a few prepared scripts, like a self-introduction, that you can say without effort.
Shadow the dialogues on this page and the listening page for ten minutes a day.
Fillers and buying time
Japanese speakers pause with sounds and set phrases. Use them instead of English “um”.
A self-introduction to memorise
Say it until it is automatic; then change the details.
はじめましてhajimemashitenice to meet you
Hajimemashite.“Nice to meet you.”Why:
エマEmaEmmaとto(quote)申しますmōshimasuam called
Ema to mōshimasu.“My name is Emma.”Why:申します is the polite version of です here.