Make sure you have JEI (Just Enough Items) installed so you can see the Solderer recipes.
A big amount of iron and quartz is required throughout the mod.
A decent amount of diamonds and gold is also required for some items.
A minimal setup
Step 1: The Controller
Craft the Controller.
The Controller is the "master" of the storage network.
This is the block where you'll be giving Forge Energy to.
Forge Energy (also sometimes called RF) is an energy unit that other external mods can generate, including, but not limited to: EnderIO, Thermal Expansion, Actually Additions.
You'll need to get that energy into the Refined Storage Controller. To do that, look at the manual of the respective mod.
Step 2: The Solderer
To make some of the items and blocks in the next step you'll need to craft the Solderer.
The Solderer is the crafting mechanic Refined Storage uses for a bunch of items and blocks.
Make sure the Controller has Forge Energy!
Step 3: Storage and accessing your items
You can craft a higher tier of Storage Disk, but for simplicity sake we're going for a 1k.
Craft a Grid to access your items.
Step 4: Done!
You are now able to insert and extract items in the Grid!
To fully understand all the blocks and items of the mod a readthrough of all the wiki pages is recommended.