1. You want to start by thoroughly watering. This will help with maintaining moisture in the root ball and breaking it up enough to not damage the roots but spread them.
2. Once this is done, dig a hole much bigger than the root base of the plant. A good rule is to have it about 1.5-2 times as wide and deep as the root base.
3. Optional: Mix into the soil some compost. This will help with supplying nutrients to the plant in its new home.
4. Place the plant in the hole. The top of the root base should be at ground level. Move the dirt (and compost if step 3 was done) into the gaps around the plant and apply pressure to pack the dirt in. Do not over pressure it.
5. Thoroughly water all the soil within 2-4 feet around the plant. This will ensure the root base and surrounding soil has enough moisture to maintain and will contribute to settling the plant into the hole.
It also helps to remove any damaged or dead roots from the root base. However, you should avoid damaging the roots and plant as every little bit helps.