When you're first starting out working with leather, you can get away with just one tool for punching holes in leather - the rotary punch. As you continue in your leather crafting journey though, you may wish to get some more specialised tools so I have described some of these below:
Rotary punch: As mentioned above, this is the tool I recommend for you to use to punch holes when making shoes and accessories at home. It is readily available at your local craft store and has multiple sized punches that rotate around so you can choose the size most appropriate for your task. To create a slot with one of these, (as will be needed in some sandals for the straps to go through the insole), simply use your rotary punch to make a hole at each end of the slot marking and then use a utility knife to cut from the outside edges of one hole to the other. (There are photos illustrating how to do this in the Silver Sands Sandals pattern instructions.)
Slot punch: If you are making many slots the same size, you can purchase a slot punch. They are, however, quite expensive and can only be used for a single size of slot. If you do wish to use one of these, you will also need a nylon, polymer or rawhide mallet to hammer the punch (a metal hammer will damage the punch), and a plastic cutting board or piece of very thick veg tanned leather underneath to protect both the surface you are working on and the blade of the punch.
Drive punch/saddler's punch: If you don't have a rotary punch you can use one of these to punch round holes and then use the same process as described for the rotary punch to create a slot. As with the slot punch, this kind of punch needs to be hammered with a nylon, polymer or rawhide mallet, and the punching should be done on a cutting board or piece of very thick veg tanned leather. Although these punches come in many sizes, each individual punch only makes one size hole so it may be more cost effective for you to purchase a rotary punch (unless you intend always making just the one sized hole).
Nylon or polymer mallet: If you are using a drive punch or slot punch to pierce holes in your insole, you will need a nylon or polymer mallet (or rawhide mallet) so that you don't damage your punch. (If you are using a rotary punch to make your holes and then cutting the slot with a utility knife, you won't need a mallet.)
Chopping board: A plastic chopping board (like the type you might use in the kitchen - but get a separate one for this purpose, don't use the one you actually prepare your food on) will protect your punching tools when used underneath the leather you are punching holes/slots in. Alternatively, you can use a piece of thick veg tanned leather (such as an off-cut of soling leather) underneath the piece you are actually punching the hole in.
If you're trying to source any of these tools, the rotary punch should be available at your local craft or hardware store, and you'll find suitable chopping boards in many supermarkets or homewares stores. The remaining tools can be found at specialist leatherwork and shoemaker's supply stores (such as those listed here).