The main piece of advice I have is to slow down the frame rate. This will be unpopular with some people, but I think for those that are actively trying to follow what's going on in the game, it's solid advice. Set the game frame rate (not the graphics frame rate) to 30. Ideally I would actually set it at 20, but this version of the game needs a higher frame rate to ensure that your keyboard and mouse inputs work properly all the time.
When the dwarfs are warping around the screen, it's hard to tell what's going on. Slow them down. Take it easy. Pause the game a lot. Look at each dwarf and see what they are doing at any given time. See what they are carrying. Use the follow mode to see them complete tasks. Look at their thoughts. Are they happy with what they are doing? Are they sad?
Another hint is to limit the size of the population in your fortress (the population cap in the options). Keep it at about 20-25. Get to know your dwarfs. Keep your building ambitions low. Make sure all your dwarfs have a place to sleep. Make sure there is a nice dining room. Make sure there is a place to socialise. Make sure there is plenty of drink and food. Get all the creature comforts set up. Then think about upping the population cap (or not!)
And finally, don't worry about it. Let your fortress grow, die and crumble. Build another one. Let the history of your world grow. Your 7 dwarfs are only 7 random dwarfs in the world. They can fail. It's fine. There is no winning in this game. Give yourself permission to make as many bad fortresses as it takes. Or more, if you enjoy making bad fortresses :-)