How do I time a run? I don't see Kosmic pressing a button to start and end runs. Is there a software I can use? If so, what is it?

I'm not sure I really understand the exact context of your question so I'm going to answer all possible contexts of it.

1. Most runners use a timer application to time their runs. The most common is LiveSplit, although there are a few others out there that people will use. All timer programs are manually controlled by pressing a preset key on a keyboard to control them and their various functions. (see below for an exception to that). This is how console runners time their runs for the most part.

2. Some games, almost always PC games, can have autosplitters which are coded by the community for the game. Autosplitters connect into LiveSplit and will automatically perform actions such as pausing when loading, or performing a split.

3. Some games will frame count top times which is the act of downloading a video (or using an online tool) and examining the exact number of frames the run took from the starting condition to the ending condition. This is done to get an exact time for the run that eliminates the human error of starting and stopping a timer manually. This is often done for console games that are extremely optimized and competitive so they can get the milliseconds of the run exactly.

I believe Kosmic actually uses a foot pedal connected to his computer running LiveSplit to split his timer manually, you'll hear the "thunk" every time he splits.