There are a couple ways to practice this.
The first is to write out melodic lines you like, add syncopation, and practice the syncopated version. For example, if you're improvising in C and you play a blues-y lick this:
Then you might try moving the first note back an eighth, so that your phrase starts a little early:
The syncopation can be added to the beginning, middle, or end of the lick. If you're not sure how to get started or what licks to write out, then record yourself soloing, and apply this exercise to the licks you play on the recording. Or, with some practice, you can reach the point where you practice this during your solo: after you play a lick that you like, play it again with some syncopation in somewhere. It's really helpful to practice so that you can hear both the non-syncopated and syncopated version in your head. After doing this enough, you'll be able to add and remove syncopation on the spot during your solos.
Some musicians who try these exercises above might feel like they're not producing licks that sound good. If you feel like you're not skilled at adding syncopation effectively, then there's something else to try. Pick an artist who is a master of syncopation. (Stevie Wonder comes to mind. He is especially good at syncopating the beginning of his phrases.) Listen to the recordings and learn to play along with the syncopated lines. Figure out which notes have been syncopated, and then try removing the syncopation and playing the lick again, so that you can feel the difference. Once you've done this enough, you'll develop a good sense of what syncopation you like and how to add it in to non-syncopated licks.