Hey,
First thing to do when joining the server would be to link up your MC account with your dogcraft.net account (
http://dogcraft.net/linkdc.php). That should enable you to interact with stuff on the server. Do keep in mind that the spawn area allows for less interaction since it's an admin claim where you can't break or place blocks.
Outside of the spawn area (there should be a message when exiting/entering spawn) you should be able to place and break blocks after linking you account.
Some basic commands:
/tpa <player> : request to teleport to a player
/tpahere <player> : request a player to teleport to you
/tpaccept : accept a tp request
/rtp : teleport to a random location
/m <player> : private message a player
/r : reply to most resent private message
/sethome <name> : sets a home at your current location (default amount of possible homes is 1 I think, in the webshop you can buy upgrades for this)
/home <name> : brings you to a previously set home
/delhome <name> : deletes a previously set home
There's also the option to claim area's. For this you need a golden shovel and claimblocks. Claimblocks accumulate during the time you are on the server or can be bought in the webshop. In the FAQ there should also be a link to a good instruction video on claiming land.
This should get you started I think. There's also a lot of warps, of which I don't know the specific names. I know there should be one to get to spawn, one to get to the endportal and one to get to the mall at least, but ask ingame if you need any of those.
Hope this helps you getting familiar with the basics of server interaction.
Have fun online!