How do I send my text logs to my email?

Open the message conversation, tap Edit, tap all the parts of the conversation you want to email, tap Forward, enter an emails address, tap Send.

It comes out as a big jumble. How do you get it with all of the dates and times and who said what?

You would either have to take screenshots of the conversation and email the photos to yourself, or use 3rd party software to extract the entire conversation, such as Touch Copy or PhoneView (Mac Only).