My friend bought a copy of the game, installed it, etc... and passed me a trial key. I also purchased the game but wanted to play around on the trial for a bit. He wanted to help out with some quests but we can't find each other. We're on the phone going: wait, so you're also on the Sol - Earth Spaceport - standing in the concourse area in front of the admiral's lift and you can't see me? what the heck.
I had a problem with that too. I couldn't see my buddy at first either until he friended me and I accepted. By the way you can give them a tell by hitting enter and going into the chat panel type /t or /tell yourfriendscharactername@their account name , your message and then hit enter. You can't just use their character name you have to use that full thing. Once your friends you should be able to see them and everything.
Every area of this game has multiple instances. The random chance of you and your friend being in the same instance at the same time are extremely remote. Once both of you are friends, you will be able to look in the instance list and it will show you what instance your friend is in if they are in the same area as you. To find the instance list, look at the top of the mini map, click on the top area that tells you where you are, it should bring up an option to change instance. If your friend is online and in the same area, one of those instances will show (1 friend) in a particular instance. If your not friended, you both can select and instance and transport there and you should be able to see each other.