Bubble sort: swap everything in order of progression until everything is in order.
Insertion sort: if data on a certain side is bigger/smaller than the value, in goes the value at that point.
Quicksort: pick a middle point, small goes on left and big goes on right, repeat until everything is in order.
Mergesort: have several arrays, divide into halves, repeat until everything is array of size 1, start combining, sort after each combination iteration, repeat until done.