I'm not an expert, but I was going through some of my notes today that native speakers told me about how to speak more naturally.
- When saying words try to think that you're saying at least two characters at once. So, when you think about saying ありがとう imagine the word in your head as あり-がとう, not あ-り-が-とう.
- If you're thinking in romaji, imagine the characters written as: と=To, そ=So, へ=He, etc... with a big consonant and a small vowel. Don't over-emphasize the vowels, pretend they're "small".
- Getting the beginning and the end of a word right is most important. In fast natural speech the middle of the word is often really quick and sloppy anyways.
- Say particles as if they're part of the previous word. So like, the が and じゃ in "日本語が上手じゃありません。” are said completely as if they're the end of the previous word.