There are as many ways to keep your research and yourself organized as there are people on earth. As long as whatever your choose works for you then it's a good way. If however, you aren't convinced your current strategy for keeping your research and yourself organized is working for you then consider Zotero.
Zotero has three main pieces that you have to set up before you can run wild saving your research.
First off, start at zotero.org.
Select Download, and then Zotero will walk you through downloading the application and the installing the plug-in. After you have installed both pieces then return to the website and register for a free account.
When you have finished that you can open the Zotero app on your computer and link it to your online account (Preferences dialog box) so that you will have your research library with you on the go.
Go to any website, article, video, etc. and click the plug-in in your browser to save that resource to your library.
Collaborate and share sources with other people through the use of Groups. You can create a group, invite people to it, and then everyone can add sources to the group library.
Zotero also integrates with Microsoft Word and Google Docs. After you have installed Zotero, open Word (or restart it if it was already open) and there should be a new menu/ribbon (depending on your operating system) labeled "Zotero". This gives you the capability to include citations directly from Zotero and Zotero will attempt* to format them for you (in your chosen style).
Zotero has a fabulous documentation site that will answer many of your questions about using Zotero.
Zotero's ability to make accurate citations is 100% dependent on the quality of information in Zotero. You can edit your sources in Zotero to include better citation information, if needed. It is still your responsibility to cite your sources appropriately.
If you aren't confident that you are citing your sources appropriately or your are concerned that you might be unintentionally plagiarizing, ask for help! Talk to your professor or make an appointment with a librarian.