There are a lot of opinions on this, but mine is that using the original IDC connectors is fine for home use, and is less likely to produce crappy crimps like the one you see on the pin third from the right in that picture. IDC is much easier to use for newbies.
If using Trifurcon terminals, however, I use a separate piece of wire and don't try to stuff two wires into the same crimp terminal. It's hard to explain in words, and I don't have pictures handy.
1. Put a piece of heat-shrink tubing on the original wire.
2. Crimp one terminal on the original wire.
3. About 2" back on the original wire, use wire strippers to cut into the insulation and spread apart about 1/8" inch, exposing the wire, but not cutting the wire.
4. Using a new piece of wire ~2" long, make a hook to loop around the exposed wire.
5. Solder the two wires together.
6. Slide the heat-shrink into place over the splice and shrink it.
7. Crimp a second terminal onto the new piece of wire.