The simplest technique to produce syncopation is to accent upstrokes (assuming you strum or pick with downstrokes on the beat ;)).
Syncopation normally also involves bringing an anticipated chord (or note) forward, off the beat. IOW, instead of hitting it on beat 1, you hit it on the previous 8th note, or the "and of 4". Because it's on an 8th note between the beats, that means hitting it with an upstroke - and also missing the next downstroke (beat 1), to highlight the fact that the chord is displaced an 8th note early.
It's often said that syncopation belongs to jazz, and it is of course a fundamental element of jazz rhythm, but syncopation is crucial to rock too. Every great rock riff (chords or single notes) is a mixture of on and off beats, the off beats representing syncopations. Keith Richard is the master of rock chord syncopation (eg Brown Sugar, Start Me Up); Pete Townshend too.
So -
1. Master your time-keeping (downstrokes solid on the beat);
2. Add upstrokes without losing the beat (hopefully you're already OK with this!);
3. Accent the occasional upstroke;
4. Omit the downstroke following an accented upstroke;
5. Whatever chord (or note) would have been on the next (missed) downstroke, play it on that upstroke before.
It's crucial to keep feeling the quarter-note pulse - the effect of "down on the beat", even if those downs are not played. In general, don't be tempted to change your hand/arm movement to accent an 8th between the beat with a downstroke. Keep the hand (and pick) moving down on the beat even when you're not hitting the beat; this will keep your time regular. This applies to all medium or fast tempos where 8ths are the smallest beat division.
At slower tempos, however, you probably WILL be strumming or picking down on every 8th (up on 16ths between); so syncopating those 8ths will of course mean a downstroke, but it's still between the beats, with the following quarter note beat missed or de-emphasised. And you can of course apply 16th-note syncopation! (That's funk... ;))