Here is an example of a very simple warmup I have my students do at the beginning of their piano lesson. I show my students how to correctly do the fingering. After C Major is mastered, we move on to transposing to other keys.
The free downloads include a pentascale (sometimes called a 5 finger scale), a one octave scale, an easy arpeggio, a simple chord progression (authentic cadence of V7-I), ending with a major triad.
These exercises should be played with firm fingertips, lifting the fingers high, without tension, at a tempo where they can be played precisely, playing only one note at a time. They can be modified to work with various articulations (staccato, portato, etc,)