I really don't like billing time for things I am not really sure how to do and need time to educate myself on. This happens more often than my wallet is comfortable with and I spend more time learning than making money. How do you go about staying in an estimate or fixed budget when something comes up that you don't know anything about?

Don't worry about it. Bill as you would usually.
You're getting paid for problem solving, not writing CSS for a button.

Learning time is a fundamental part of knowledge work.

This is not an assembly line where you should turn out 10 resistors a minute.

You can't possibly know everything. You will always be looking up stuff.

Just like lawyers, they don't know the whole law by heart, every line. They also have to look it up and figure out how they would use it in your advantage.

They pay for your knowledge how and when you acquire it has nothing to do with them. Bill bill bill

agree with the above. to us a task, even one we need to learn a bit for, may seem simple. but the people paying us would never be able to do it so...

I guess I look at it from my own perspective as a small agency owner. When I sub out work to freelancers, I don't want to pay for the time it takes them to learn a new JavaScript library when I expected them to know JavaScript based on what their resume or Freelancer.com profile says. In fact, is suspect I got that treatment recently with a PHP dev I hired to build a Wordpress plugin I couldn't deal with. It was way more expensive than it ought to have been based on other work I'm familiar with in the same vein. Most of the freelancing gurus I'm reading (Danny Margulies, Danielle Greason, etc.) say you should only bill the productive hours.

@stackodev True, does depend on the working environment