To start, hold a tasty treat in a closed fist and show it to the puppy. Say nothing but wait until she gives up trying to take the treat from your fist and pulls her nose back. As she does this, quickly present her with a treat from the other hand. Do this several times until she is reliably moving her nose away every time that you present a fist to her.
For the next stage, uncurl your fingers. Be prepared to clamp your fist shut again if she makes a move towards the treat. As you give her the reward from the other hand , say 'take it'.
Do this for several training sessions before moving on. This is a behaviour that needs to be hard wired, so don't rush each stage.
You will notice that no cue word has been added yet. I like the dog to work out for herself that she needs to reject the treat in order to receive the reward.
When you feel that she is ready for the next stage, put a treat on the floor close to your foot. If she makes a move towards it, quickly cover the treat with your foot. It is important that she never succeeds in getting the treat, otherwise she will believe that it is worthwhile carrying on trying on the off chance that she may be successful.
If at any point she does manage to get the treat, take the training back a stage and don't move on until you can be sure of success.
After a while she will back away from a treat placed on the floor, then you can move outside.
Set up a line of temptations and with her on a lead, walk parallel to the line. Make sure that if she moves towards the line , the lead is short enough to prevent her from reaching the items. The lead should be loose as you walk. Do not say anything or pull her back. If she moves towards an item, stop and wait. She will realise that she cannot reach the object and after a while, will turn to look at you. When she does this, present whatever are her biggest rewards . Use really great treats, squeaky toys or a quick game. She needs to know that turning away from something that she wants will bring her greater rewards.
Once she is walking along the line of temptations without a second glance, you can up the anti.
While she is on a lead, throw a piece of food ahead of you but be prepared to root yourself to the spot if she makes a move towards it. Other people can offer her a treat in an open hand but if she moves towards it before you say 'take it', they must close their fist.
It is only when I am confident that she can do all of this that I put in the cue "leave it". I say it in a happy voice as she turns away from an object that she desires and I really reward that dog.
Leaving the command until this late stage is the way that I have found works best for me. It means that I am using a cue for a behaviour that is already well in place. Traditionally, you would add the cue at the very beginning when she moves her head away from the closed fist. Do whatever you think will work best for you.
I occasionaly walk through an area where there have been rumours that bait is left down for foxes. Although my dogs have good "leave it" skills, I take no chances and keep them close by me at all times. If I had no choice but to exercise them in such an area, I would use basket muzzles. No method of training is 100% successful and even 99.99% would not be good enough for me in such circumstances.
If your dog already has entrenched 'not leaving it' skills. Go back to basics and use a different word as a cue. Remember that she will get better at anything that she practises, so if she is allowed to practise running off with someone's picnic........