Getting the Varrock Armor in RuneScape is somewhat time consuming, especially if you want to get the Varrock 3 set. Yes, like some other RuneScape armor sets, there are three different levels of Varrock Armor. The steps outlined below list how to get the first level of Varrock Armor.

Runescape Varrock Armour
Completing the Varrock Achievement Diary

Complete the following requirements to finish the Varrock Achievement Diary. You can do some of these in any order, although you will need to complete step 1 to begin the diary quest.

1.) Speak to Rat Burgiss (south of Varrock), Reldo (Varrock Castle), or Vannaka (Edgeville dungeon). Ask any of them what the achievement diary is.
2.) Go to Thessalia in Varrock and ask her what different outfits your character can wear.

Runescape Thessalia

3.) Visit Aubury's Rune Shop and have him teleport you to the essence mine.
4.) Mine iron ore south-east of Varrock
5.) Create a plank using the sawmill. You will need a plain set of logs and 100 gold.
6.) Visit the Stronghold of Security and go down to the second level.
7.) Leap the fence just to the west of Rat Burgiss.
8.) Go to the Lumber Yard and cut down a dying tree.
9.) Buy the Varrock Herald for 50 gold from Benny.
10.) Give a bone to any of the dogs in VArrock
11.) Create a bowl on the pottery wheel and fire it in the oven in the Barbarian Village (you must be in the village).
12.) Go to Edgeville Dungeon via the entrance located south of Edgeville.

Runescape Edgeville

13.) Speak to the Varrock estate agent and have him more your house portal. This will cost 5,000 gold and you must already own a house.
14.) Obtain 50 kudos and then talk to Haig Halen, the Varrock museum curator.
15.) Use an earth talisman or tiara to visit the Earth Altar.
16.) Visit Varrock's church and offer Elsie a cup of tea. Listen to her story.
17.) Mine limestone near the Paterdomus temple east of Varrock.
18.) Go to the river located to the east of the Barbarian Village. Fish until you catch a trout.
19.) Go through the Varrock Sewers until you find a web and then slash it.
20.) Go to the highest point in the city of Varrock by going up to the Church's third floor.
21.) Return to Rat Bugiss
Conclusion

That's all it takes to get the Varrock Armor 1 set. If you lose it, just speak to Rat again and he will give you another set. The armor gives you better discounts from Varrock merchants, gives you the chance of mining two ores at once while mining, and gives you the chance of smelting two bars instead of one when smelting. Once you have the Varrock Armor 1, you can then begin the next list of tasks to get the Varrock Armor 2 and then Varrock Armor 3.