How you run varies a lot by country.

In the US, you start by filing papers to do it. Typically a combination of a fee and collecting signatures. Municipal government tends to have a lot of power over things like what commute mode is favored and local building codes, so I recommend it for first-time candidates. You'll need to raise enough money to help get the word out, spend a lot of time visiting community groups and talking with people, and ideally recruit a few volunteers to help you win a primary.