A guitarist has exactly the same problem as you do. If you just strum the chord on the downbeat, or on every beat, it sounds boring. You have to play more interesting patterns.
The guitarist does have a couple of advantages over a pianist in this respect. Early on, a guitarist learns to get more rhythmic interest out of a basic chord, by varying the rhythm of strokes, and by muting. Some of these effects are more difficult on a piano, and some are impossible.
The simple guitar chords a beginner learns are in a variety of inversions, so that level of interest is added "automatically" to a beginner's guitar playing.
At the very basic end of what a guitarist might also do:
Inversions - play the chord at a different position on the fretboard; or simply begin the strum on a different string.
Arpeggiation - very common for guitarists; break the chord into a sequence of single notes. Typically you'd go up for 3 or four notes (depending on time signature), then back down to the root.
Rolls - right-hand patterns that are more complex than an arpeggio. A common one is the classic blues/folk pattern where the bass strings go from the root to the fifth on the 1st and 3rd beat, while the remaining strings are played as a chord on the 2nd and 4th.
Connecting notes - you're going from a G to an F? Play an F# on the way down.
Of course, from there, there are plenty of variations. Learn by copying.
But you're on a piano. Fortunately, all of the above have direct equivalents on a piano keyboard:
Inversions - instead of putting your thumb on the root note and playing the 3rd and 5th, put your thumb on the 5th below the root you're playing, then the root and 3rd above that. You have several octaves' worth of notes to pick from.
Arpeggiation - I don't really have to explain, do I?
Rolls - the closest analogy to the guitar roll I described is a classic boogie-woogie piano part, where the left hand does the root-to-fifth-below bass part, and the right hand plays choppy chords in various inversions on the off-beats. There are lots of "learn to play boogie-woogie piano" books on the market.
Connecting notes - as easy (or easier) on a keyboard as on a guitar.