How do you deal with someone who seems unable to explain what he needs?

Where to find a communication board

There’s something called a communication board. It’s often used for people who are non-verbal, but it’s not exclusive to those people. It shows a variety of pictures of everyday things.

https://www.communicationcommunity.com/how-to-make-a-communication-board/

I found that they have a problem with getting the right word. Mom was trying to tell me something about her bra but bra was not the word she was using. It is very frustrating but something they can't help. Brain is all jumbled. Just listen to what is being said. You will probably get good at figuring out the wrong word. Its as frustrating for them as you.

And to add to MJ1929s comments. It’s always good to check vitals and weight. Keep a log. Then you will know some of the things they can’t express.
If there is a reason he might be in pain, a recent fall, a loss of appetite, change in bowel habits, etc, then take appropriate action, within reason. Then watch for improvement or seek appropriate help. By keeping a log you can tell when there is a trend.

Not to disrespect an elderly person, but think like you're dealing with a small child.

Use the process of elimination --
Does something hurt? Yes/No
Is it your head? Hand? Arm? Stomach? Leg? etc. etc.

Are you hungry? Yes/No
Are you thirsty? Yes/No
Do you want something hot/cold?

Are you hot/cold? Yes/No

Can you tell me what you see? Yes/No

And so on. With any luck, you'll eventually find what's bothering them, and you may learn the signals that mean different things to him, just like children's cries are different for different things.