Generally, you can still work out with mild muscle soreness (slight pain or a mild sting when flexing the muscle). What's key here is making sure you properly warm up the muscles involved. After warming up, you should be able to perform at your full capacity even with a bit of soreness.
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Now, if you’re experiencing severe muscle soreness (to the point where doing everyday things like sitting down on the toilet is barely doable or causes intense pain due to the soreness), it’s best to cut your muscles some slack and let them recover instead of working them in your next session. In this case, you can just skip the exercise(s) that target the sore muscles and finish your workout without them.