Below is an example Turnitin report. This report is a fairly unrealistic test of the system - it would be hoped that the vast majority of your essay would be original work, and that the matches with the internet or other sources would only total a few percent, depending hugely on the subject material. Departments with a mathematical or other precise component often give a higher percentage score (more matching) because students sometimes have no option but to include the precise procedure; however originality is required whereever possible in all academic work.
The whole idea of students being allowed to submit work to Turnitin themselves is so that they can see for themselves where they are getting matching with other people's written work and so they can find out for themselves how to construct an academic essay properly. Everything you write must be written in your own words, be properly referenced, or, where a particular piece of text is part of the common knowledge for the subject, but cannot be attributed to an individual, you should explain that you know that you are using this text and why you're doing it.
More advice on how to write essays properly is given here, and courses on writing essays can be found here . Anyway, back to the report. A description of its various parts are below:

The new Turnitin mechanism shows all the formatting and any images, so what you see should look like your essay on paper. To show any matching, you need to click on the red "Originality" button at the top left, and any matches will show up as overlays, with the colour and number of the match the same as the colour and number of the web address, student paper or journal location where the match was found.
Turnitin compares your work with on a scan of the internet - a search like Google's for each phrase of your essay, then it compares it with the content of their library of journals and then it compares it with other student essays that have been submitted to Turnitin. Where matches are found, the text is highlighted as mentioned. The mechanism can get a bit confused if there are quotes in your quote, as shown above, and it doesn't look like it's very predictable what it does when it's confused. Turnitin isn't a precise tool - it's best used as a general means of pointing out that there might be a problem. If you're worried that you've done something wrong, you'll just have ask your tutor to put your mind at rest.
Your lecturer will have set up your Turnitin submission space so that you can upload work over and over again until the due date, with a 24 hour delay enforced between submissions (enforced by Turnitin, not us; we'd make it less time if we could). By repeatedly submitting your work, you can therefore use the submission area to make sure that all of your work is original, and all of your references have been correctly declared by the time that you hand work in, though you'll have to have your initial essay done a few days before the due date so that you can submit work to Turnitin enough times that you can be sure that you've got all the improper references and accidental matches with existing texts edited out of your work.
Incidently, if you look to the bottom right of the report, you can see a thing that looks like an upsidedown triangle. If you click on it, it shows options to include quoted areas and the bibliography in the list of matches. Your lecturer will have set up Turnitin so that properly quoted references and the bibliography don't get included in your matching score. If you unclick the links so as to include references and the bibliography, and recreate the report, the increase in matches will be the proportion of your work that are references. (It'll take another few minutes to make the new report). If more than 15% of your entire essay is references, your essay is going to look like it's lacking in original content, and you maybe should work on increasing that content.
A video by Turnitin that goes through the reporting facility very well, and shows extra facilities can be reached by this link: http://www.turnitin.com/static/support_video_gallery_instructor_viewingor.html
Although your lecturer is certain to have told you this already - self-submission might look like a good opportunity to cheat and get away with it, but it isn't that simple. Copied beginner and intermediate essays can often be overlooked by busy lecturers marking piles of work, but copied dissertations later in your student career won't be. The task of creating a dissertation is just too complex for you to be able to slip bits in that you got off the internet and the lecturer will know your work too well by then and will be looking for anomalies, because it's such an important piece of work. Using Turnitin for Student submission is done as an exercise in writing better essays, and if it isn't used for this, it will be much more difficult to complete that dissertation properly later on. People who try to plagiarise parts of their dissertation will probably get caught, and this will mean a large reduction in the overall degree grade.