To start agility you want to talk to the Gnome Trainer at the Skilling Area (accessed via the Location Teleport in your spellbook).
He will Teleport you to the Gnome Stronghold Course.
Complete the course as shown in the picture to the right.
Do this course until you are level 52.
One you are level 52 you will want to move onto the Wilderness Course. (THIS IS A PVP ZONE BE CAREFUL)
To get to the Wilderness Course go to your mage book, click Wilderness Teleports,
click on Mage Bank, Pull the lever at mage bank, and run West until you see an agility icon.
You will want to utilize the Wilderness Course all the way to 99 agility.
Experience Table
Wilderness Course(Gnome isn't significant)
Regular Experience - 90k xp for iron man/legend
Regular Experience - 600k xp for regular accounts (sir's)
Double Experience - 180k xp for iron man/legend
Double Experience - 1.2M xp for regular accounts (sir's)
x4 Experience - 360k xp for iron man/legend
x4 Experience - 2.4M xp for regular accounts (sir's)
The Math
For IronMan/Legend Info(did not do time for Regular)
1-99 on a Double Xp weekend with vote book is about 14 minutes to max.
1-99 with only either Double Xp weekend or a vote book is about 28 minutes to max
1-99 without any bonus experience is about 36 minutes.
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52-99 is 12,910,771 experience this means the following
Regular accounts - no bonus - 22 laps
Regular accounts - x2 bonus - 11 laps
Regular accounts - x4 bonus - 6 laps
Iron Man/Legend - no bonus - 144 laps
Iron Man/Legend - x2 bonus - 72 laps
Iron Man/legend - x4 bonus - 36 laps
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lvl 52-200M xp is 199,876,340 experience this means the following
Regular accounts - no bonus - 334 laps
Regular accounts - x2 bonus - 167 laps
Regular accounts - x4 bonus - 84 laps
Iron Man/Legend - no bonus - 2,221 laps
Iron Man/Legend - x2 bonus - 1,111 laps
Iron Man/legend - x4 bonus - 556 laps