If you are relatively new to Minecraft, Tekkit can be rather daunting to new players. It might be best to learn a bit about the vanilla version of Minecraft before you play around with all of the plugins on the server. There is an excellent list of tutorials available on the Minecraft Wiki:
If you can give those tutorials a run-through, you will be well on your way to mastering the vanilla version of Minecraft.
Eagleworld also has a great selection of plugins available to enhance your mulitplayer experience, such as Essentials, LWC (Lightweight Chest Protection), and more! You can type the command /help at any time to see the list of commands you are allowed to use. Make sure to type /help 2, help 3, help 4, etc. to see all of the commands listed, page by page. You can also do /help and the name of a command to see help about that specific command. For example, /help tpa tells you how to use the teleportation command.
Also, don't forget that your chests are automatically protected by LWC. if you want to see how to work with the chest protection plugin, use /lwc help to see all of the commands available!
Thanks to Essentials, getting around Eagleworld is extremely easy! There are ways to easily teleport around to warps, home bases, other players, and more. Here's the list of important commands to get you started:
Warps and Homes
/spawn - Teleports you to the Petros Tower in Capitol City.
/warp - Allows you to see the list of warps on Eagleworld. Type /warp warpname to go to a specific one.
/sethome - Allows you to set your home warp. You can always type /home to get back to it.
/sethome name - Lets you set a different warp. Higher-ranking players can set more homes for themselves. Type /home name to warp to a specific home.
Teleporting and Players
/tptoggle - Lets you turn on or off teleportation requests from other players. Note that Mods and Admins can override this.
/tpa player - Architects and up can request to teleport to other players. The other player has to type /tpaccept for it to work.
/tpahere player - Architects and up can request that other players teleport to them. The other player has to type /tpaccept for it to work.
/tp player - VIPs can teleport to other players without asking, as long as the person did not disable with tptoggle.
/tphere player - VIPs can teleport other players to them without asking, as long as the person did not disable with tptoggle.
Tekkit is a bundle of plugins all installed on top of the Bukkit server wrapper that greatly increases what you can do in Minecraft. There are many plugins installed, such as IndustrialCraft2, RedPower, ComputerCraft, BuildCraft, Equivalent Exchange, and more that not only make your day to day tasks in the game easier, but give you much more to work for. I've compiled a list of the best tutorials here.
Basic Tekkit Tutorial - This is intended to be an overall tutorial for Tekkit, but is not yet comprehensive. It heavily favors IndustrialCraft, but is planned to be updated.
First Steps in IndustrialCraft - This tutorial will show you how to build up in IndustrialCraft and not only generate energy, but build a nice group of appliances that will assist you in mining and resource gathering.
Comprehensive Equivalent Exchange Tutorial - This tutorial will give you an excellent linear path of progression through the EE items, and allow you to quickly ramp up to generating a lot of items quickly!
Hold your Hand through BuildCraft - A great tutorial on the BuildCraft wiki which can get you started working with pipes, and ultimately starting your own quarry.
ComputerCraft Tutorials - A great hub of tutorials on all things ComputerCraft.
RedPower Recipe List - A good page that provides all of the RedPower recipes!
Other Tekkit Wiki Tutorials - This page on the Tekkit Wiki links you to many more good Tekkit-related tutorials, including working with Nuclear Reactors, generating diamonds, etc.
Other BuildCraft Wiki Tutorials - This page on the BuildCraft Wiki holds all the tutorials available there. They can help cover more in-depth information that the Hold you Hand tutorial did not.
I highly recommend checking each of the Wikis for the different tutorials on them. There are many great tutorials available which can explain most of the important stuff in the game!
Lastly, here are excellent links that everyone should be familiar with. Tekkit and each of their major plugins have excellent Wikis which provide extremely in-depth information about all of the new items and recipes available to you: