You choose one domain. You get one bonus slot of each level to prepare each domain spell. In addition as a storm druid, you can spontaneously cast any of your domain spells instead of another spell you prepared.
You get to choose one domain from a list of five options (Air, Weather, Cloud, Storm, Wind; the last three are subdomains, which are just specialized versions of their parent domain).
You get to add the domain spell to your known spells of the appropriate level for free when you first gain a level that can cast spells of the specific level. So if you have the Air Domain, you get Wind Wall (level) at 3rd level when you first gain access to second level spells. You can memorize this spell as a normal spell, but you're better off with the other option.
As a storm lord, you can 'spontaneously cast' your domain spells, instead of the normal things a druid can spontaneously cast. This means, you can cross off a spell you have memorized, such as entangle, and instead of casting that spell you cast a domain spell of equal or lower level.
For example, you're a level 4 druid with the Air Domain. You have the domain spells Obscuring Mist (level 1) and Wind Wall (level 2). You have prepared the following level 2 spells: Bull's Strength, Heat Metal, Wood Shape. If you need to cast Wind Wall, you would say "I'm spontaneously casting Wind Wall in place of Wood Shape". You would cross Wood Shape off your list of prepared spells for the day and then cast Wind Wall as normal.