Fermentation is a process (metabolic) that converts sugars to alcohol and CO2 (and some other products). So, yeast  converts glucose from wort, the result is alcohol and carbonated beer. 

Main yest types are 2:
1. Ale (Saccharomyces cerevisiae, top fermenting yeast) – fermentation at higher temperatures (approximatelly 20 °C / 68 °F) and shorter fermentation period (approximatelly 2 weeks)
2. Lager (Saccharomyces carlsbergensis, bottom fermenting yeast) – fermentation at lower temperatures (approximatelly 10 °C / 50 °F) and longer fermentation period (approximatelly 6 weeks)

We also know Spontaneous Fermentation: exposed beer  – natural, wild yest, bacteria infects beer and fermentation starts.

How to do in practice?
No problem, let’s do it:
When you have cooled the wort to end point (Ale approx. 22 °C / 71,6 °F; Lager approx 18 °C / 64,4 °F) you can pitch yest to fermentor. There are three important things to know for good fermentation: 
– good aeration (do it by splashing cooled wort at cooling, mixing of fermentor, air injection)
– enough yest (if you pitch to much you will get sour and yest taste beer, if there is not enough yest, fermentation will be inhibited)
– start temperature can be a little higher than yest should ferment at.

Here are few videos of fermentation (Ale and Lager) at specific hours/days from pitching: