I might suggest reading up on regular expressions - they are kinda critical for what Splunk does. But, to get you started...
| rex "Client IP \[(?<clientip>[^]]+)\] with username \[(?<username>)[^]]+)\] connected successfully to server \[(?<server>[^]]+)\], resource \[(?<resource>[^]]+)\]"
Here's how this is supposed to work. Within regex, [ and ] denote a set of characters. So, [aeiou] will match a single vowel -- a, or e, or i, or o, or u. Putting a ^ as the first character of the set says "match anything not in this set". The + means "one or more of these", and we escape (backslash) the [ and ] when we mean them literally. So, \[(?<clientip>[^]]+)\] means something like "an open square bracket, followed by one or more of anything that is not a closed square bracket, followed by a closed square bracket." The wrapping of (?<clientip> .... ) says to assign the field name clientip to what's inside the parentheses.
Now, go read http://www.regular-expressions.info/ and get up to speed 🙂
