The first example is just in one colour and is simply a foundation row followed by the pattern. This is formed with slip stitches throughtout, alternately in the front and then back loop of the rows beneath. The placement of these is by setting your own pattern if you want but this description is for the top one pictured. 1st to 3rd rows the stitches of the pattern would be in the back loops and on the 4th to 5th rows the stitches of the pattern would be in the front loops. 6th and 7th rows would continue in the back loops and then 8th to 15th alternate 3 stitches in the back loops with 3 in the front ones. Stagger one stitch to the left in each row of the pattern so as to form oblique stripes. 16th to 17th rows are in the back loops with 18th and 19th in the front. The 20th row finishes with back loops. If you want to create your own pattern, mapping it out on grid paper is often a good idea.
The braid in the second example above does require plotting and is created by changing shades. The entire work is in slip stitch in the back loop. Both of these braids are quite difficult to work (hence their toughness) so a fine thread yarn is preferable although I have made this in a 4-ply cotton.