An in-depth guide is available here, written by Feeds.
Summoning; is a skill that focuses on calling familiars from the Spirit Plane by creating and using summoning pouches. Each familiar has a unique ability that requires a Summoning scroll, made from a corresponding pouch, to use.
Familiars have a wide variety of uses, from fighting in combat to carrying items to providing invisible boosts to other skills. Summoning is a fast skill and will take very little time to achieve a 99 mastery.
To begin Summoning, go to your magic spell book and click on the More Skilling Teleport. Head over to where it says Summoning, and click it. As you travel to this new place, you will make your way to a swampy looking area, but around you are two shop members with similar needed items for Summoning. These shop members are named Pikkupstix. There is also a shop member named Dommik who sells Summoning scrolls. To begin you'll want to click on the Summoning Obelisk which will tell you how you will make your familiars. You will need the following:
Spirit shards (packs)
Here is an example of how to begin Summoning. Head over to the Summoning Obelisk and click on the first familiar called Spirit Wolf. It will give you a short description of the items needed in order to begin. Head over to Pikkupstix and purchase one shard box, a few pouches, and a few wolf bones. This is just so you will guarantee to level up faster. (few). Next, you will need charms, which you would most likely get from your starter pack when you first joined. If you hadn't or used them up previously, you can go to the ::slayertower and collect charms there. You only need one a few gold charms for this. Gather those charms and go back to the Summoning Obelisk. Click the spirit wolf. Right click your Spirit wolf pouch to summon it. Want to dismiss it? Goto the bottom of your tabs beside your emotes and view the summoning wolf. Click it, and press dismiss familiar.
Below is the quickest way to get to 120 Summoning.