Let the soil in the pot dry-out a bit. This keeps the rootball intact during transplant. Moist soil crumbles.
Prepare the new pot with drainage and fresh soil.
Turn plant upside down with the trunk between your fingers. Give a little 'whack' to the bottom, and catch the plant as it slides right out. Be careful with the tops while you're doing this. I've broke a couple by not paying enough attention to the plants length.
Turn upright, and place in fresh pot. Gently massage a few of the roots out of the rootball to let them know there's fresh meat available. Don't fold, spindle or mutilate the roots, but should look like it's having a bad hair day in a couple spots along the side.
Fill in with fresh soil, gentle pressure.
Water deep with properly ph'd water.
Add more fresh soil to the voids watering created, but leave an inch or so at the top of the pot. This leaves room for future feeding and watering.

Also, don't leave the rootball exposed and go answer the telephone or hit the store for munchies. Shouldn't need to rush things, but don't dawdle either.