K.D.
Oh, how familiar this sounds! My daughter is now 4, but I still remember VIVIDLY the incredible tantrums she had at 12 months. She was a slow talker, so, developmentally, she was probably equivalent to your 10MO. And it was SO frustrating to have no recourse - timeouts were not appropriate and verbel reasoning would have been ridiculous to try! Furthermore, NO ONE I knew had ever seen a 12MO with tantrums like this.
I spent my days trying VERY hard to keep things "pleasant". If my daughter wanted a non-toy item that wasn't necessarily "dangerous" - like an empty coffee mug or the remote control - I let her have it (with non-stop supervision). I devoted my days to her for a few months - no dishes, no laundry, certainly no cleaning! If she was struggling at a playdate, I ended it. If she couldn't handle grocery shopping, I left. I also worked HARD at ignoring other people's stares and comments - many people will have advice for you, but it will apply to two-year-olds, not infants! I'm not sure if my high level of attention actually helped her, or if it just helped me keep my sanity, but either way, we both survived.
As much as possible, I tried to prevent the tantrums. I know, HOW??? That will come to you in time - each child is different. Until then, HOLD HIM when he's upset. He is so little, and his emotions are so big, he needs someone to help him control himself. If he's thrashing and won't let you hold him, at least stay nearby. Put a hand on his back if you can. Talk or sing low and quiet. Be consistent and do the same thing every time. Once he calms down a bit, sign and talk to him. "You were very upset/angry/frustrated. I love you. I want to help." Give him a hug. He needs to feel secure until he can start to understand these crazy emotions. You will not see immediate results! Give it 2-3 weeks before you try something different. Consistency is so important - give it time to work.
I came to the conclusion that my daughter desperately wanted to communicate with me, but was struggling tremendously. We DID do sign language - it helped. Include signs for emotions too! Within a couple months, your ability to communicate with each other will improve dramatically, and that is the light at the end of the tunnel. Note that the tantrums might not stop - but you'll have a better feel for when and why they are likely to happen, and what kinds of things you can do to help him. Timeouts can start at 18 months, but be careful. There is a difference between having strong emotions and poor behavior. You should never discipline a child for having emotions.
Definitely keep your sense of humor! Times like this are exactly when you need to remind yourself of all the wonderful traits your son has. Write it down when he makes you smile. Read the list often! It will help give you perspective for the next tantrum.
Let us know what worked for you, so the next Mom has a few more ideas!
Good luck, K.