the Achievement Diary can be started by speaking to Explorer Jack inside the house you came out of. He will tell you the things above. He later goes on to explain that the Green Star icon is the diary icon. You can click this and it will show this:
Lumbridge/Draynor
Beginner
Easy
Medium
to view these, click on "beginner" and do the things it says. Then, after you do all the beginner Achievements, you will get the "explore" emote and an explorer's ring!
