On to or Onto

On to is used when on is part of a verb phrase.
Onto talks about movement from one place to another place.

• She held on to her hat.
  (verb phrase/held on)
• First, I need to log on to my laptop.
• The dog jumped onto the sofa.
  (from one place/the floor – to another place/the sofa)
• He climbed onto the wall for a better view of the sea.