String patterns
Oh do I love these things

You're going to want to extract it using string.match.

local FirstH1 = HttpService:GetAsync("http://www.example.com/"):match('<h1>(.-)</h1>');

Why does it work?
string.match takes two arguments - The string to match against, and the pattern to match with. Because the string library is inherited by all strings, match can be called as a method of a string. This in turn means that the returned string is implied as the first argument. The pattern is therefore the 'first' argument, which works like so:

• <h1> matches

• ( ) is a capture. This is the part that match returns when it finds it.
• . matches any character.
• - matches the preceding set 0 or more times, using a non-greedy matching: It will match as few occurrences as possible to satisfy the pattern.
• </h1> matches