Obtaining specific dimensional information about a PCB is another commonly requested item. How long/wide is the board? What are the diameter of the holes? Where are the holes? etc.

In the primary Learn Guide for a product, so called "Fab Prints" are provided, typically in the Download section at the end of the guide. For example, here's the one from the BMP280 guide.

These fab prints will have some general overall dimensional information. Maybe that has what's needed? If not, then the dimension tool in Eagle can be used to try* and find the desired information.

*Eagle's dimension tool is very klunky and crude. Don't expect modern day CAD style dimensioning functionality.

Start by activating the dimensioning tool.

Click the Dimension icon in the toolbar.
This will bring up the dimension tool options in the top menu.
Set Units to desired value.

There are several specific options depending on what is being measured. Select one using the appropriate icon in the top bar. Use horizontal or vertical for basic dimensioning. Use radius or diameter for circle/hole/drill dimensioning. Use angle for any angles of interest.

Horizontal

Set start point of first leg.
Set start point of second leg. This also defines the dimension length.
Set location of dimension label.

Vertical

Set start point of first leg.
Set start point of second leg. This also defines the dimension length.
Set location of dimension label.

Radius

Set center location.
Set radius by clicking any point on circumference. This defines the radius value.
Set location of radius label.

Diameter

Set start location on circumference.
Set opposite start location. This defines the diameter value.
Set location of diameter label.

Angle

Set apex location.
Set a point anywhere on first leg.
Set point on second leg. This defines the angle value as well as the dimension label location.

Snapping Behavior

No one fully understands Eagle's snapping behavior when using the dimension tool. Just punch your way through it as best you can.

If you find you can't quite get the two dimension points you're attempting to measure, consider turning off layers that don't apply to the desired measurement so you have better access to the two points you're going for.

Hole Specific

For any hole (drill, via, etc.), it's generally easier to use the information tool to get the size (diameter). This may require accessing the part in the Library Editor. Here's a simple example for a via.