Firstly, you need to arrange a comfortable sitting position for pruning because miniature rose bushes are usually low. If you prune while bending over, not only will you get tired quickly, it will also be harder for you to consistently prune the bush. Ideally, the roses should be at eye-level when you work on them, so getting an appropriately sized bench is recommended.
When it comes to tools, you will need a pair or pruning shears and a rake for the project. Unlike full size roses, the miniature variety requires more precise pruning, for which thin, narrow blade shears are recommended.
Before you begin, you will need to plan the pruning. While most people start at the top and thin the bush down to the bottom, you can also start from the bottom, cutting away at the thick canes and twigs and cleaning up the bush. It is important that you actually know the look you want to achieve before you start working on it.
Start by cutting away at the brown growths and cleaning up twigs, which are thinner than your little finger. Clearing this up will allow you to have a better view of the thicker canes and cut them up more easily.
When cutting the thicker canes, you need to aim to remove the top 1/3 of its length. It is recommended that you clip a cane just above a new bud-eye. You will also need to remove the foliage since it is going to fall anyways.
Now you should focus on cleaning up the rose bed. Remove all weeds in and around the rose bush and use your rake to clear up debris from the bed.