Understand the different phases of R.E.M.'s work. Like many players, Buck's style can be divided into distinct eras--starting with the jangly yet clean sensibility that characterized their early to mid-'80s work. To pull off that tone, combine a Vox AC30 amplifier and semi-hollow-body Rickenbacker guitar.
Check online guitar sites--and early classic albums, like "Murmur"--to get a feel for the chords that Buck favors. Typically, he sticks to major chords (A, C, D, E, G)--leavened by the odd minor ones (A minor, E minor) for contrast purposes--and major scales, on those rare occasions when he solos.
Don't confine yourself to basic strumming, and leave it there. When you're holding down chords, allow for the odd open string to ring out for a bigger sound. And, although he rarely solos, Buck is known to pick out arpeggios on individual strings for greater textural variety.
Study closely how Buck blends acoustic and electric guitars, which he's done from REM's earliest recordings. Don't worry about recreating them exactly--to approximate the sounds of multiple guitars, employ a chorus delay pedal (as heard on "Life And How To Live It").
Tackling the sound of later period albums like "Monster" (1994), or "New Adventures in Hi-Fi" (1996) requires a simpler, more stripped-down approach. Switch to the classic combination of a crunchy Les Paul guitar, and run it through Marshall amplifiers.
Experiment freely with effects and tunings--as Buck did on "E-bow the Letter," whose title references the sustaining device that he combined with a Drop D tuning (achieved by tuning the top string to a D-chord pitch). Round off the sound with fuzz distortion pedals.
Consider the quirks of the amplifiers and guitars that Buck uses. For example, nailing the urgency that characterizes an album like "Monster" requires the overdriven sound of a tube amplifier--versus solid state models like the Vox AC30, which tend to dampen the sound. (To get around the latter problem, turn up the treble function.)
Try contrasting tempos and textures. Much of R.E.M.'s musical subversiveness is grounded in confounding expectations--such as the cheery chords that ring out on an angry classic like "What's the Frequency, Kenneth?" for example.