One of the common uses of the particle か is often translated to ‘or’ in English. While this translation is accurate, it is not actually any different from か’s regular usage as a question marker.

• それはお母（かあ）さんの靴（くつ）かお父（とう）さんの靴（くつ）。
  Are those mom's shoes, or dad's shoes?
• それはお母（かあ）さんの靴（くつ）か。お父（とう）さんの靴（くつ）か。
  Are those mom's shoes? Dad's shoes?

From these examples, we can see that, in Japanese, か is performing the same role that a question mark would, or that a change in tone of voice would in spoken language.
‘Would you like tea? coffee?’ (said with a rising tone)
This nuance of か can be used after the dictionary form of almost any word in Japanese. However, using です or ます will change the nuance from ‘presenting possibilities’, to ‘asking a formal question’, so should be avoided.

• 今日（きょう）か明日（あした）休（やす）むか。
  Today or tomorrow, when will I take a break? (The speaker is thinking this to themselves)
• 今日（きょう）か明日（あした）は休（やす）みますか。
  Will you take a break today or tomorrow? (The speaker is asking another person)