You must be talking about herpes simplex, the virus causes by cold sores, you may be able to transfer the virus especially drinking after them or kissing on the lips. If you are talking about herpes zoster usually known as chicken pox but often on adults known as shingles you should avoid the same linens, towels or pillows if the breakout is in the draining stage. If you are talking about sexually transmitted herpes, you should never have unprotected sex and even then with or without a condom during an outbreak you can get them. It lies dorminant under the skin so a condom even if your partner has no breakout could be risky. Same goes for using the same towels or anything that touches the area especially during a breakout. You didn't say which Herpes you are talking about but either way you still must be careful. Any of the Herpes viruses are highly contagious in certain forms so just be careful and always use good common sense.
Since genital Herpes is at an all time rise, know you sex partner and if you do and are in a monogomous relationship and say, he has them but you don't, just be very CAREFUL. He will understand. There are many happy married and unmarried couples where one or the other person has them, yet the other doesn't. Having the affected partner on Valtrex or another anti-herpetic medication you have a good chance of never getting them if you avoid sex during an outbreak and always, breakout or not, use a condom. Good luck. AND no you cannot get genital Herpes from a drinking cup. If you a have a cold sore refrain from oral sex with him. Even though they are "different" strains they are highly contagious either way.
Good luck and hope this helps!