It's easy to feel helpless around someone who's crying. And some people with Alzheimer's are capable of crying often.
What to try:
Recognize that there's some kind of emotion inspiring the tears. Speak to it directly: "You seem very sad. Can you tell me what you're sad about?" Even if your loved one can't articulate what's behind the tears, it's useful to provide the opportunity to give voice to the feelings. He or she may then cry harder, and that's OK -- it's expressing the emotion.
Respond warmly. You can say, "It seems like it's hard for you to talk about this. That's OK. Just know that I love you and care about you."
Provide ongoing verbal and physical support (a hug, a shoulder rub) without feeling like you have to solve the issue.
Monitor for other signs of depression, which often (but not always) occurs with dementia. Learn the warning signs of depression in someone with dementia.