There are a few different ways for you to access and use Mendeley. Each link will lead you to the appropriate site when you decide which works best for you.
Download Mendeley Desktop: this is the actual program that allows you to organize PDFs and sync to your online account. It is compatible with Windows (7, 8.1 and 10), Mac (OS X 10.10 and 10.11) and Linux.
Mendeley Online: from here you can sign into your account, import citations straight from databases, access your libraries from anywhere, and sync to your Mendeley Desktop.
Web Importer: add this to your bookmark toolbar and you can import citations directly from databases and websites to your Mendeley library. This page also lists the companies that are compatible with the importer.
To export your citations from Mendeley, you need to:
The ris file of your Mendeley library is ready to be imported into another citation manager.
Mendeley Desktop is the downloaded part of the software installed onto your computer. Mendeley Web (also called Mendeley Online) is the website to access the online version of your library, edit your profile and search for papers, groups or people. You can also access Mendeley's social features.
Mendeley Desktop excels at ingesting PDFs and automatically creating citation data from the information in the PDF. Mendeley desktop also offers excellent features for managing your PDFs on your computer as well as searching and viewing them.
Mendeley Web allows you to access your saved research on the go (depending on how much of your data you decide to sync) and collect citations while browsing online databases. Mendeley Web will also ingest PDFs from a very small selection of journals, but this is neither widely supported nor very reliable. Mendeley Web also provides access to "largest crowd-sourced research catalog" via its Papers collection.