Append

To add a measure to the end of the piece press Ctr+B (Mac: ⌘+B). To add multiple measures use the menu Create → Measures → Append Measures....

Insert

First select a measure then press Ins to insert a new empty measure before the selected one. To insert multiple measures use the menu Create → Measures → Insert Measures....

Delete

First select the measure then press Ctr+Del (Mac: ⌘+Fn+Backspace).
For 0.9.5 and earlier, it's different. Press Ctr (Mac: ⌘) on the keyboard as you click on an empty part of the measure with the mouse. The measure is marked with a dotted line indicating that you selected a "piece of time". Press Ctr+Click (Mac: ⌘+Click) to extend the selection. Pressing Del (Mac: Fn+Backspace) removes the selected measures.

Properties

To edit the properties of a measure right click on an empty part of the measure and select Measure Properties....

Staves

The Visible property allows you to show or hide the notes and staff lines for the current measure. The Stemless property allows you to show or hide all note stems for the current measure. Notes that normally have a stem such as half notes (minums) and quarter notes (crotchets) only show the note head when marked as stemless.

Duration

The Nominal duration is the time signature that is displayed on the score. You can change the Actual duration of a measure to anything regardless of the time signature displayed on the score. Normally the nominal and actual duration of a measure is identical. However a pickup (upbeat) measure for example can have a shorter actual duration.

In the figure below the quarter note (crochet) pickup has a nominal measure duration of 4/4 but an actual duration of 1/4. The measures in the middle have both nominal and actual durations of 4/4. The complimentary measure with only a dotted half note (dotted minum) at the end has an actual duration of 3/4.

Irregular

An "irregular" measure is not counted in the measure numbering. Normally a pickup measure is marked as "irregular". If you are using version 0.9.4 or earlier and mark a measure as irregular then you may need to save and reload the score before the measure numbers show the change.

Repeat count

If the measure is the end of a repeat you can define how often the repeat should be played.

Break multi-measure rests

This property separates a multi-measure rest at the current measure. If the current measure contains a change of time signature then MuseScore marks this property automatically.

Numbering

MuseScore automatically numbers the first measure of each system but more numbering options are possible. From the main menu choose Style → Edit Style. In the left pane choose "Numbers". In the bottom half of the right pane is the "Measure Numbers" ("Bar Numbers") section.

Mark the checkbox next to the "Measure Numbers" ("Bar Numbers") to turn on automatic measure numbers.
Mark "show first" if you want the first measure numbered.
Mark "all staffs" if you want numbers on all staffs, otherwise only the top staff of each system shows measure numbers.
Choose to show numbers on "every system" which numbers the first measure of each line, or show numbers by "interval" and specify the size of the interval. For example, an interval of 1 numbers every measure; an interval of 5 numbers every fifth measure.