The loop start only works if the design needs and even number of strands, i.e. 2, 4, 6 etc.
For the areas that need two strands, you only need to use one strand because when you fold it in half, that makes two strands. So as Brigitte said, thread your needle posting the two "ends" through the eye of the needle. Now, when you look at it, you'll see two strands threaded on the needle with one end being "uncut".
Now, make the first arm of your cross, come up through the first hole leaving the "uncut" part of the strands at the back, like what you'd do if you used two separate strands, then finish the first arm by going through the second hole as you would normally do (first arm makes a half cross stitch) but when you go through the back, put the needle through the loop 9which should also be at the back), then pull the needle further to finish the first arm and this will make the loop secure at the back with no trailing ends to catch.
The website below has a good tutorial. If you are making lots of cross stitches you only need to follow items one to eight.
http://www.better-cross-stitch-patterns.com/loop-start.html
So, then when you need to just use one strand you will have to do what you normally do, i.e. catching the thread underneath your stitches as you go.
Hope this makes sense.