There are really several ways of testing snort, some much more complex than others. Probably the most simple way is to define a custom rule that you can easily produce the traffic to trigger the alert. This can be done by creating a simple rule that looks for traffic of a certain type, to a certain address or many other ways but for the purposes of this article we will be looking for traffic to a certain address (as this tends to be the most easily produced). We begin by creating a custom rule either in a new rules file or by adding the rule into an existing rules file. To simplify this you can download the rule from the url below:
Once you have downloaded this rule file and added it to your snort.conf so that Snort has loaded it, simply generate traffic from the monitored network to one or more of the following hosts: 18.104.22.168,22.214.171.124,126.96.36.199. This traffic can be of almost any type. I will typically browse via browser or telnet to a standard IRC port (at the time that I wrote this, these hosts were on the known C&C list) such as 6666, 6667 ....
Once this is done you will see the alerts being generated by snort (assuming that everything is configured properly).
As a second method, you can attempt to generate traffic that an existing snort rule can detect and alert on. To do this, I suggest using a tool such as Metasploit to generate actual attack traffic. You will want to test it against a host that you own, I certainly am not advocating attacking someones network with Metasploit from your network, this host should either be intended to be a test host, and/ or be immune to the attack. A simple example would be to enable the web-iis.rules from snort.org and launch an attack against one of your patched webservers from metasploit in an attempt to exploit MS01-23 using the Metasploit Framework Exploit. This will in-turn generate the WEB-IIS ISAPI .printer access alert to fire.
Either of those two methods should allow you to test your Snort installation, there are some other tcpreplay type tools that you can generate traffic from some signatures with, but by and large they are not effective tests.