To download: Open up webpage by clicking on the button, or go directly to https://qgis.org/en/site/forusers/download.html. Then choose between the latest release with the most features (QGIS 3.10.1 'A Coruña') and the stable, long-term release (QGIS 3.4.14 'Madeira'). I'm not sure whether it makes much difference.
What it's good for: Manipulating vector and raster datasets; projecting and presenting geographic data.
What it's not great at: Style; can't do interrupted projections; can't really work with text.
To sign up: Click the button or go to this link https://signup.earthengine.google.com/#!/. You'll be asked for an organization affiliation and what you're using the program for. The people at Google will review your sign-up submission and will grant access once they have verified you're not pursuing commercial interests or something. Afterwards, you will be able to work with maps and data at https://code.earthengine.google.com/.
What it's good for: Working with satellite data, image collections and feature collections, performing calculations, working with dynamic data that changes over time, etc.
What it's not great at: Projections (it works in Mercator), can't really do text, it's somewhat hard to import/export images.
Where to find: Lab computers in Armstrong Library, here on the 6th floor of BiHall, and in Sunderland 122.
What it's good for: Manipulating vector and raster datasets; projecting and presenting geographic data. Has some projections, such as Fuller, that are unavailable in QGIS. Might be more intuitive to use than QGIS.
What it's not great at: Style; can't do interrupted projections; can't really work with text.
Access: On lab computers you should be able to sign in with Google, which will open up a webpage for verification via Middlebury username and password
What it's good for: Working with text, editing points, lines, and polygons (vector graphics), getting artsy/creative.
What it's not great at: Editing raster graphics (images in pixels) – for that, see Adobe Photoshop, also available on lab computers with Middlebury login.