Although I have an account in both sites, I use only Facebook to promote my business so I can tell you my opinion from that perspective only.
First at all, most of the people start connecting with old friends. It is something that you cannot avoid since you will receive invitations because they have your email or are looking for you with the friend finder utility. Sooner or later you will do the same until you feel that most of your friends have been found.
In the meantime, you can learn all the features: Creating Goups, Events, Pages, Causes, Advertising, Pay Per Click and Applications Adding (which is also an addictive and the most powerful way to promote your business).
To promote your business you can create a group. You may choose between creating a group for your company or for your business area. The difference is huge, a company-related group means that you created it to make business and a business-area-related group means that you are there to provide information and help. The business comes later when you establish a relation of trust with people in the group. Remeber that most of the people are in Facebook for fun not to make business.
Invite your contacts to join your group and ask them to invite their friends, which is a viral way to promote your group. Some others will join the group when they see that a friend of them joined the group. It appears on the news feed of their profiles
If you have events, create an event and invite your contacts. Join other groups related to your business and communicate them that you have a group where they can find good tips.
Join some other groups and participate. Write anything every day since any actions you take is communicated to your connections. They will see you every day and will want to know what you are doing.
You can also create a page and promote it. Although pages can also create posts, get members and some other things, people prefer to join groups more than pages.
The last one, but could be your first one, if you are developer or have someone who can do it for you, is to create an application. Create something fun that people want to join. You will be able to have their information if they allowed you, place AdSense and, of course, place your business on it. The application is distributed in a viral way because people invite others to join and then, you will have a community to market your business. Be sure to create something related to your business.
Remember that you are there for fun too
so be carefull of becoming addict
, because it is addictive!