I was induced with both of mine. My first, my waters broke and labour did not start so I needed the oxytocin drip. For my 2nd, she was overdue.
The first "step" is you'll check in and get given a suppository which is meant to help prepare your cervix (if your cervix is not yet soft/ready for labour). Sometimes that is enough to start labour by itself. If it is, that is definitely "easiest". If not, you may also require an oxytocin drip. For my 2nd, I had the suppository and things were getting started just with that, but then my water broke again before my contractions were regular or strong, so I went on the oxytocin drip in my 2nd delivery as well.
I would prefer to avoid the oxytocin if possible - at the public hospital, if you are on the drip, they won't let you get out of the bed so it is hard to move and get comfortable. If you want a drug-free delivery, that restriction would make it near impossible. Both times, I didn't really mind whether it was drug-free or not, but I got an epidural both times mostly because I couldn't get comfortable since I wasn't allowed to move. The epidural helped me to be able to sleep through much of the labour.
Anyways - if you have any more specific questions, feel free to ask or PM me if you prefer...
Nicole