The best way for a drummer to lead worship is for them to learn guitar or piano.
I know that isn't the answer you are looking for, but the truth is you need to be able to lead others in singing and sometimes, especially when you are starting out you might be doing that solo. While some bands can be lead by a drummer, the easiest way to lead others is in the front.
If you want this to be your career you really have to be able to lead others with your voice and an instrument. Put the time in.
Also if you want to get experience quickly, look for church plants in your area and message the pastor there to see if they would be willing to let you work on your skills there as a volunteer.
Source: am a drummer, but also play guitar and sing. Have played for several churches as a staff member leading worship.
Jonathan recommends the following next steps:
- Learn guitar and/or piano.