^ is the beginning-of-line anchor, so it will be a "zero-width match," meaning it won't match any actual characters (and the first character matched after the ^ will be the first character of the string). Similarly, $ is the end-of-line anchor.
* is a quantifier. It will not by itself match anything; it only indicates how many times a portion of the pattern can be matched. Specifically, it indicates that the previous "atom" (that is, the previous character or the previous parenthesized sub-pattern) can match any number of times.
To actually match some set of characters, you need to use a character class. As RichieHindle pointed out, the character class you need here is ., which represents any character except newlines (and it can be made to match newlines as well using the appropriate flag). So .* represents * (any number) matches on . (any character). Similarly, .+ represents + (at least one) matches on . (any character).