Help! My dog turns into a lunatic when excited!

I think the key phrase here is "10-month-old puppy", LOL!  It's pretty normal.  I have to say that I think your trainer's advice to stand on the leash is bad advice.  You're just going to make the dog try that much harder.  Yes, when approaching strangers or friends who don't feel comfortable around dogs, keep the leash short to avoid unwanted behavior until the dog is properly trained but keep in mind you're just keeping someone from being "attacked" by the dog, but teaching the dog nothing.  If all you do is stand on the leash, the dog will never stop TRYING to jump, that needs to be trained out of them. You can try teaching "off", but I've found with my dog she'll listen to that command but it does nothing to keep her from jumping over and over again.  When the dog jumps, turn away, don't give it ANY attention.  If she's jumping on someone else, and won't stop, I find a squirt bottle to be very effective.  For nipping that occurs while petting or playing, give a firm "No bite!" command and stop playing with/petting the dog, then resume giving affection when the dog calms down... I also usually give a redirection with nipping, putting a toy or bone in the dogs mouth.  Scout always used to chew on our hands when we gave her belly rubs.  We figured out that what makes her the happiest dog in the world is to get a belly rub WHILE having something fun to chew on
 
With the jumping while playing, it helps to learn the cues that your dog is ABOUT to jump.  My dog gets this crazy look in her eye, like she's going to pounce on a rabbit or something, then takes a flying leap.  I've learned to be ready, so I turn around and kinda stick my butt out, so she just crashes into my backside
 
Keep in mind that none of this will happen overnight.  Dogs generally have a strong urge to both nip and jump until they're fully mature, which can vary by breed, but it lasts until their AT LEAST a year.  However, by continually discouraging the unwanted behavior you will make progress as time goes on. 
 
 

This video could help, click where it says "Boo"
 
[linkhttp://www.dogpsychologycenter.com/dogwhisperer/showclips.php]http://www.dogpsychologycenter.com/dogwhisperer/showclips.php[/link]
 
 

Thanks for the feedback.   Here is why I stand on the leash vs just keeping her on a short leash.  If I dont stand on the leash she jumps on me too and its hard to stop a dog from jumping on you when you have them on a short leash.   If I stand on her leash, she corrects herself when she goes to jump and generally calms down after a few minutes.  
 
Last night I was convinced she was the devin spawn but of course she was as sweet as pie this morning.   So it goes.
 
In brighter puppy news,  we have been focusing on her recall lately and she stopped mid run towards something fun yesterday and came back to me!  She loves those tiny little pieces of hot dog! 

Standing on the leash is *fine*, so long as you are also teaching her the command "sit" as an alternate behavior to jumping up.  Remember to give no attention whatsoever (even eye contact) to a jumping dog.  Just step on the leash, give your signal for "sit" and only pat or pay attention to the dog if she is calm and sitting on her butt.
The reason people get into trouble is that they "give in" and either talk to, shove, push, say "off", etc., which the dog interprets as a reward for the naughty behavior. 
Once you start stepping on the leash and/or ignoring her when she is jumping, you may get an "extinction burst" where her behavior actually gets worse.  She is operating on the idea that her jumping always got her some attention before, so she will try even harder.  Once that doesn't work, however, the likelihood of the behavior "extinguishing", or going away, is much greater. 
Unfortunately, all your family and guests must be on the same page with this, as intermittent failure to ignore her will reinforce the jumping up.  Bottom line, you need to be consistent.
The worst thing to do is any physical pushing or shoving, or tightening the leash (the reason for stepping on it is so you don't yank it).