How can I remove all characters up to and including the 3rd slash in a string?

To get the last item in a path, you can split the string on / and then pop():

var url = "http://blablab/test";
alert(url.split("/").pop());
//-> "test"

To specify an individual part of a path, split on / and use bracket notation to access the item:

var url = "http://blablab/test/page.php";
alert(url.split("/")[3]);
//-> "test"

Or, if you want everything after the third slash, split(), slice() and join():

var url = "http://blablab/test/page.php";
alert(url.split("/").slice(3).join("/"));
//-> "test/page.php"

var string = 'http://blablab/test'
string = string.replace(/[\s\S]*\//,'').replace(/[\s\S]*\//,'').replace(/[\s\S]*\//,'')
alert(string)

This is a regular expression. I will explain below

The regex is /[\s\S]*\//

/ is the start of the regex

Where [\s\S] means whitespace or non whitespace (anything), not to be confused with . which does not match line breaks (. is the same as [^\r\n]).

* means that we match anywhere from zero to unlimited number of [\s\S]

\/ Means match a slash character

The last / is the end of the regex

var str = "http://blablab/test";
var index = 0;
for(var i = 0; i < 3; i++){
    index = str.indexOf("/",index)+1;
}
str = str.substr(index);

To make it a one liner you could make the following:

str = str.substr(str.indexOf("/",str.indexOf("/",str.indexOf("/")+1)+1)+1);