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:
What is your "calling" to worship ministry, and how does it align with what a church wants from their worship leader? I thought I was called to be a worship leader since that's what everyone said I was good at since I was a 6th grader. When I got my first worship leader job (right out of college, thankfully), it only took me 3 months to realize this was not what God had in mind for me. I've been called to help people explore their faith through growing their own creativity—whether that's through music, film, photography, software development, hospitality or something else!
Worship leading, at the end of the day, is about 2 things—good music and team effort. Although most people expect certain things out of worship leaders (i.e. "you should be able to sing and/or play guitar/piano!"), I suspect that excellent, localized worship by the church and for the church is really what people are after, regardless of the size of a church.
If you want to make a career out of being a worship leader, then you should have a working knowledge of *all* the instruments in an ensemble, not just drums, vocals, guitar and piano. You should love to work with people, and you should learn to shepherd the people you work with and for.
KJ recommends the following next steps:
1. Leadership. Surprise! Of course, you are leading an entire group of musicians, and you need to be able to gather them all together and lead them in the way the music needs to go. So basic leadership skills are quite necessary. In the same manner, you will be leading the congregation through the musical part of the service, so you need to have the kind of presence that keeps people with you.
2. Ability to take direction. Just the opposite of #1, I know. But your job is to enhance the church service through music, and in order to do that, you need to be in tune with what the church leadership wants to do. So you'll need to be able to take direction from the ministers or whomever is in charge of the service.
3. Composition. Many churches create their own original music based on the teachings or spiritual direction of the ministry. Nearly all worship leaders I know are composers. In addition to composition, you may need to lead or guide others on the worship team who are also songwriters, so a knowledge of composition is important.
4. Singing. If you're gonna lead, you've got to be able to sing. And that's gonna mean melody AND harmony. As part of the leadership role, you'll need to direct the other musicians in their parts - especially helping singers find their harmony parts and rehearse them.
That being said, you're going to have difficulty leading worship from behind the drums. That's just a logistical fact. So it may be more appropriate to be a music director WITHOUT being worship leader. Or perhaps for a number of services you do not play drums, and lead worship instead.
Hope that helps.