Do you know what size my handlebar has? I want to buy a new pair of Tektro brake levers and I do not know what steps to take about it
You need to measure the grip area diameter (the diameter of the handle bars where the brake levers clamp onto). I'd suggest using a pair of calipers.
22.2 mm will fit flat bar (typically mountain bike/flat bar road) components, 23.8 mm will fit drop bar (typically road) components.
Note that you need to also get compatible pull brake levers -- in your case, you have a caliper brake so you need a short pull brake lever (ie. one that is marked for not linear pull/V-brakes).