I desperately need to teach Oliver to leave it/drop it and I have no idea how to even start.

My silly beagle boy snarfs things up off the ground before I even see them and I've had no luck getting him to stop before he eats them. In fact, I think my desperate attempts to get whatever he has out of his mouth likely makes him swallow it even faster than he normally would. He's made himself sick twice in the last 2 weeks from, I think, gobbling up something from the back yard (I can't figure out what it is).

I have no idea how I taught Jack to do this; it just sort of happened naturally. When I say "Yuck!" he spits out whatever he has in his mouth or backs away from whatever he was about to pick up. I never consciously taught him to do this. In fact, I didn't consciously teach him much at all.

Oliver has had no training. Plus, he always thinks he's absolutely starving to death so he tries to eat anything he comes across. I pulled out an old clicker (Jack is terrified of the sound so we never got anywhere with clicker training, and never really needed to) but we're at the very beginning and total novices. I don't have a lot of hope that we could learn "leave it" any time soon on our own.

The next beginner class at my local training school doesn't start until November, and they don't teach "leave it" until the second level. I really like to get a jump start on this, for the sake of Oliver's tummy and my carpets.

Does anyone have any advice? I don't have a clue where to even start.

I usually teach it with a toy get them to take the toy then say "drop" and give them a juicy treat.By opening to eat the treat I'm presenting, they drop the toy. I quickly tell them that was awesome and say "get it" and give the toy back or toss the toy if it's a dog who loves to run after it.
The idea being that they get to have what they dropped back and in addition they get a treat. That makes it a no brainer to drop on cue. Then the odd time when I can't give the dropped object back doesn't seem like a big deal. You see some dogs who never get to have the dopped object back and their respoonse to "drop it" is to swallow faster.
You can start with relatively low value items and work up to more importnat things, practice in a variety of places too.

I taught Nutmeg by having a piece of food in my fist. She would sniff, sniff, sniff but the fist remained closed. As soon as she turned her nose away from my hand I opened my fist and she got the treat. She learned pretty fast that leaving the hand alone brought the treat. You can do the same thing with a treat on the floor... cover it with your foot until he looks away, then remove your foot and let him have the treat. We progressed to the point now where if I drop food on the floor and say "Leave it!" she won't touch it.

I think some trainer (Kathy Sdao? Jean Donaldson?) calls it "Doggy Zen"

I've heard that called "no mugging" "doggy zen" "off in hand" and is the beginning of part of my "leave it" but different from "drop it" in that a drop it means basically spit it out vs don't take it. Probably both reallygood things for Mr. O to learn

Yes, Mr. Oliver definitely needs to learn to do both, spit it out and don't take it. Thanks so much for these ideas. He has shown absolutely zero interest in any toys I've offered him since I got him, but I'm sure I can find something that he'll hold in his mouth.

I think, once we get the hang of it, he's not going to be that hard to teach in general. Last night when I was giving him some treats before bed, I pulled out the clicker and clicked before I gave him each one. It took about 3 times before he was looking at the hand with the clicker when he wanted the next one, and when I grabbed my mp3 player later (about the same size/shape as the clicker) he thought he was getting treats. Jack ran and hid downstairs, didn't even want treats if that awful clicker sound was happening!

Teaching him to leave food alone, though....that's going to require real work from both of us. He's soooooo convinced he's starving, though he certainly hasn't lost much weight since I got him!

Poor Jack. Do you have an i-click? They make a very soft click. I also find my timing better with it. You can teach all this with a marker word instead of a clicker too.
I'm sure Oliver will get it, you just have to make it seem like you can control the world ie if food flies off the counter and you know he's going to get it say "get it!" as if you planned to give it to him.

oh- I meant to say youtube has some videos of people teaching all of these.

I used a highly valued treat, put it under my foot and would show it to the dog and say "off" (I like all my negative words to be one syllable and good words to be 2 or more). She would try to lunge for it and I would put my foot over the treat again, and say "Off" I kept doing this until she got bored and sat down and looked away. Then I took my foot off and said take it. I kept doing this until she understood what "Off" meant and take it meant. After that just say off she would almost spit the object out of her mouth. For the first little while I would take the object she had (RMB) and say off...take it from her and give her a great treat then hand back the RMB and say take it. This way she associated that off might mean something better coming her way.