If you need a dildo, you can go to the store and buy a carrot, banana, or cucumber. These have the advantage of being able to through away when you're done without having to worry about cleanup, though they might be a bit large for a beginner. Other options include pens, markers, or sharpies. There are other options, of course, like the handles of tools or hairbrushes, but be careful not to pick something too big. If you're not sure, pick something smaller than you think you'll be able to take. Remember, don't let your eyes get bigger than your ass. I will instruct you on putting two fingers inside yourself, so your toy shouldn't be too much bigger than two fingers in width. Avoid sharp things.
Butt plugs are harder to improvise. You're looking for something with a tapered point, a tapered neck, and some kind of flare at the end. If you don't know what a butt plug looks like, google it. Many hairbrushes with smooth handles would work. The picture on this page are two examples of hairbrushes that would work. You can use a long dildo if you are willing to hang on to the other end if you absolutely can't find anything, but you won't be able to wear it under clothes or use both hands.
If you're not using something meant to be a dildo, you should make sure to cover it in a condom, so if you don't have any on hand, make sure to grab some at the store too.
If you're going to buy a dildo, look for ones meant for anal. If you're going to buy a butt plug, look into getting a training set with increasing sizes.