Stopping one's internal dialog is the aim of meditation. It is not easy, but it is rewarding.
Don't let thoughts stay with you, let them into and out of your thoughts like waves in a stream. This is generally practised alone, but the ability is very useful throughout one's day.

Secondly, if one must carry on an internal conversation, do it in the first person, not second.
Instead of thinking things you have been told ("you're not smart". "you're not pretty enough" ) speak to yourself as I, and you won't say the same things. Take any internal conversation and make it first person ("I am better than that. " I am proud of what I have accomplished" ). You mind find that you address yourself with more compassion than you would for some obscure "you" person that others talk about.
This is a long long process. Very little happens over night, but one thing that can happen right away is the change in the respect you give yourself internally. You know you've earned it.