The best way not to be tongue-tied is to plan ahead. Although you certainly don't want your words to sound rehearsed, having a preplanned sentence or two already composed in your head will be of great relief when the time comes to offer your personal condolences.

Saying nothing is not an option. You have to offer some words of comfort, even if it is as simple as "I was so sorry to hear about __'s death. It must have been horrible for you." These words will often open the door to good conversation about the deceased. It is important for the bereaved to talk about their feelings; let them talk. Offer a hug as needed.

Many people offer the standard "Just let me know if you need anything" but these well-meaning words are useless. In their grief, they won't remember what you said and call you, but if you instead offer "Do you need me to (pick up the kids, mow the lawn, help with acknowledgment cards), you will actually be helping a great deal. In the following weeks, call and offer other help, like picking up the dry-cleaning or grocery shopping.

"How are you coping today?" is a good open-ended question that will help the person express their feelings.

How about these phrases:

"Your (mother, father, sister, brother) was such a kind person, and always had a story!"

"I'd love to take you to (lunch, dinner) next week and share memories."

"You look like you could use a hug and maybe a shoulder. Can we get together?"

"I'm going to miss (him/her) in my life. I learned so much from (him/her).

"I can't begin to imagine your sadness. I am just so sorry."

When in doubt, hug.

Words to avoid include: "I know how you feel." No, you don't; everyone grieves differently. "He's in a better place now." Sometimes safe, but avoiding this phrase might be a good idea. "You'll get over it." Don't even go there. "Did he have insurance?"
"What will you do now?"