Here's a big long regex for matching a URL:
(?i)\b((?:(?:[a-z][\w-]+:)?(?:/{1,3}|[a-z0-9%])|www\d{0,3}[.]|[a-z0-9.\-]+[.][a-z]{2,4}/)(?:[^\s()<>]+|\(([^\s()<>]+|(\([^\s()<>]+\)))*\))+(?:\(([^\s()<>]+|(\([^\s()<>]+\)))*\)|[^\s`!()\[\]{};:'".,<>?«»“”‘’]))
The expanded version of that (to help make it understandable):
(?xi)
\b
( # Capture 1: entire matched URL
(?:
(?:[a-z][\w-]+:)? # URL protocol and colon
(?:
/{1,3} # 1-3 slashes
| # or
[a-z0-9%] # Single letter or digit or '%'
# (Trying not to match e.g. "URI::Escape")
)
| # or
www\d{0,3}[.] # "www.", "www1.", "www2." … "www999."
| # or
[a-z0-9.\-]+[.][a-z]{2,4}/ # looks like domain name followed by a slash
)
(?: # One or more:
[^\s()<>]+ # Run of non-space, non-()<>
| # or
\(([^\s()<>]+|(\([^\s()<>]+\)))*\) # balanced parens, up to 2 levels
)+
(?: # End with:
\(([^\s()<>]+|(\([^\s()<>]+\)))*\) # balanced parens, up to 2 levels
| # or
[^\s`!()\[\]{};:'".,<>?«»“”‘’] # not a space or one of these punct chars
)
)
These both come from this page, but modified slightly to make protocol properly optional - you should read that page to help understand what it's doing, and it also has a variant which only matched web-based URLs, which you may want to take a look at too.