Conquest is a rotating weekly set of objectives for you to participate in. Here is a link to upcoming conquest targets and objectives.
Conquest helps earn the guild not only name recognition but Encryptions that the guild can use to unlock rooms on the Guild Flagship.
What’s in it for you? Bragging rights, titles (if your guild is #1) and a handful of rewards, but mostly it’s about doing conquest objectives with your friends and guild-mates.
Here’s how to get started.
First, open your Codex
Then go to the Conquest tab
The red area, section A are the mission objectives.
Here you will find what you can do to earn conquest points. To learn what the objective requirement is, click an icon and in the window below the objective will be displayed.
In the image above I clicked an icon (outlined in yellow) and the objective below is to Defeat Trapjaw. Notice the tiny 
X that indicates this objective is NOT repeatable. The 1000 indicates how much killing Trapjaw was worth.
Now lets look at another objective
In the image above I clicked another objective, this one offering 1,500 conquest to complete heroic missions on Nar Shaddaa. There are 2 things you need to look at carefully with this objective:
1) Below the objective icon, next to the points offered is the infinity symbol. This indicates that this objective is repeatable.
When you click a repeatable objective, the bottom of the objective window will also say: 
2) In the objective window it also has a Guild Invasion Bonus!
Because our guild is invading Nar Shaddaa we will receive x3 the points for this objective. Those without the invasion bonus get only 500 per Heroic. So each Heroic completed on Nar Shaddaa are worth 1,500 points due to our bonus! Multiply that by the handful of Heroics you can do there and you’re looking at some seriously good contribution points! And that’s ALL without PvP!
The yellow area, section B is the Conquest Leaderboard
This has the running total of the current, up to the minute scores for the top 10 guilds competing (as well as the giant header of the guild who conquered it last week).
The purple area, section C is your contribution to the overall guild score.
The conquest goal is typically 20,000 but can be lower or higher depending on the week. This box also shows the planet your guild is invading. If it says : NONE next to Guild Invasion, the invasion target has not been set yet. Be patient with GM’s they’re human and have lives too. It can sometimes be a little while before a target is set.
There are a couple of things to note:
1)To the right of “Conquest Points” is the time left to contribute for the week. Most guilds make a final push once it gets down to just hours left. You will need to make sure that if you are crafting for this week’s conquest that you have logged in and received the crafted item from your companion before the clock runs out or it will not count for conquest.
2) Below your bar of contribution is a “Stronghold Bonus”. You are given up to 100% bonus (doubling any points earned) for having a decorated stronghold. Since you are allowed up to 4 strongholds, each one gives you 25% bonus when completed. As you can see in this window I have 78% bonus. That’s 3 completed strongholds and one partially done. If you want stronghold bonus, decorate, decorate decorate!!
TL:DR
Check the objectives, don’t be discouraged if you don’t want to PvP there’s always crafting and other adventures.
Watch for Guild Bonuses for objectives, maximize your conquest contribution by doing those objectives!
Above all, have fun and thank you in advance for your contributions!