I would recommend using LinkedIn as just one tool in your networking portfolio, but to start with, think about your objective with LinkedIn. Are you looking to find a job? Gain more connections to help you in future work or work search? From there, you can do as another person answered above; search out specific industries or companies you are interested in and follow them. Try connecting with recruiters if you want to find about how to get hired by those companies. Make sure you use easily searchable keywords in your headline if you are looking to get noticed by recruiters. Participate in discussions, like and comment on people's articles and updates, and participate in groups. All of these things will get you noticed more on LinkedIn.
Also remember to use it when networking in person. LinkedIn can be used as a database of your connections. When you meet someone in person and ask for their business card, email them as a follow up and also add them on LinkedIn if they have it. The site can be an easy way to update your connections when you find a new job, relocate, get a promotion, or anything else.
Thats a great initiative on your part. I will recommend searching for companies in industries you are interested in. Then, you can get started with adding recruiters who work directly with the company and not a third party recruitment agency. You can also add people in your area if you are not looking to relocate. The quickest way to build your contacts is by signing up with your current email, be it work or school email and it will show you recommendations based on those contacts etc.
If you want you can submit a request to me on linkedin to get started.
All the best.