I trim Olivia's hair myself with scissors, but I do keep her hair almost floor length, so I have no clue how clippers would work on a little one like a yorkie. Scissors work good for me, I cut with them across using my fingers as a guide (like you'd trim up your bangs.) I make a center part down her back before cutting, even though the part magically goes away as soon as we're done. I only cut when she's sleepy, and I wont touch her head or face for love or money.
You ask about clippers too. I just cut my mom's mini schnauzer's hair for the first time. I used clippers with the longest guard setting, but I had to cut the longer hair down a little shorter before I buzzed it. Go SLOW and be veeery patient
But the golden advice is this: do it OUTSIDE if it all possible, and do not attempt to do it alone. and GOOD LUCK
I don't know how short you want "short" to be, but here's a pic I made Miss Livvy wake up for so you can see my handiwork. Hope I helped!