To become a healer in Puddleby: you must convince Master Hekus you are worthy by collecting three items that are given to you by people scattered around town.
Once you are a healer, you will be able to train with several more trainers specific to healers. You will also have access to a library and a testing area where you can prove you've advanced far enough to become a second circle healer.
Eva: Eva is an all round trainer. She gives you a little bit of everything, including all the other first circle healers plus Horus and Awaria.
Faustus: Faustus trains you to heal others faster. This has the side affect of draining your health and spirit faster.
Sespus: Sespus increases your total spirit. This means you wont be drained so fast when healing others. Also, you'll be able to gain health faster when slightly injured.
Respia: Respia improves the rate that you regain your spirit at.
Higgrus: Higgrus increases your total health. He does not affect your defence.
To advance beyond the first circle you have to pass a test. The test is to raise Glory while you're being attacked by several creatures. The test to advance to the second circle consists of 2 Giant Vermine and 2 Large Vermine.
The second circle:
Sylpha: With enough training with Sylpha and a Sylphstone ring, you can heal yourself without holding a moonstone. 30, is needed, I think. The ring costs 250 coins.
Horus: Horus training helps you raise people who are badly fallen.
Awaria: With Awaria training, you'll gain more health when you heal yourself.
Three Night Wendecka and one Greymyr will be trying to keep you from raising Glory this time.
The third circle:
Hardia: Similar to Bodrus. Trains in strength all round. Capped at 300.
Proximus: Improves your ability to use a Caduceus or Mercurial staff.