How do detergents get in hydrophobic membrane interior?
It depends on the concentration, but at higher concentration the detergent molecules build so called micelles, where the hydrophobic "tail" is orientation into the inner part and the hydrophilic "head" is orientated to the outside. This allows the micelle also to fuse with the membrane and then to desintegrate it.
This illustration from the Wikipedia shows the schematically:



Its from the surfactant article, which has more details.