How do white blood cells get from vessels to the damaged cells where bacteria are?

White blood cells are extremely flexible.

A blood cell could shape itself in order to go through blood vessels.

When it reaches bacteria, it "eats" it. Its outer cytoplasmic "cover" wraps the bacteria, and transport it to the inside of the white blood cell.

 When the bacteria is inside the white blood cell, the bacteria dies because of what the white blood cell sends to it.

They attach to the endothelium of the blood vessle and crawl along the vessle untill they find the bacteria where they engulf the pathogen

Blood vessels increase their diameter and permeability in the area of damage. This increases blood flow to the area and allows defensive substances to leak into tissue spaces.
Within one hour of injury, the white blood cells appear on the scene. They squeeze between cells of blood vessel walls to reach the damaged area where they destroy invading microbes.
Functioning cells or supporting connective cells create new tissue to replace dead or damaged cells. Some tissue regenerates easily (skin) while others do not at all (cardiac muscle)