Making a carvable cake

Freeze the cake - it carves much, much easier. Make sure and wrap it tightly before going into the freezer, otherwise it may pick up odd freezer smells easily though.

Carving cakes is an advanced skill. Don't be frustrated if it doesn't work from the first time. Start with easy designs - no curves with tight radiuses. Maybe you will also want to start with a 2D shape instead of a 3D. Always make a sketch first. And start it early enough that you can re-bake if the first time doesn't work.

For the recipe, you want a dense and moist cake. A pound cake will work well. Use a 1:1:1:1 fat:sugar:flour:eggs ratio by weight, add the whole eggs to the creamed butter/sugar mix. Else, search for a recipe which is designed specifically for carving. Don't make a sponge cake or any recipe which works with egg foams, they are much more fragile.

Bake your layers roughly in the shape you'll need - for a frog, you might want to use one normal sized pan for the body and a separate small pan (or tartalette pan) for the head. The legs would be very hard to carve separate from the body, consider creating them in some other way. Carve with a sharp long knife with a kind of sawing/shaving motion, removing layers of the surface to achieve the shape you want.

It is also advisable to look at tutorials first. Youtube has lots of them, search for words like "carving cake", "sculpting cake" and "tutorial" or "lesson". Note that some of the great looking sculptures shown there need about a personweek of effort by an experienced carver, and set your goals accordingly.

As has already been mentioned -- start with a fairly solid cake; most cake recipies are not intended for carving. If you're looking to use a boxed mix, you can typically add a packet of instant pudding in with the cake mix to make the cake more dense. (don't add any extra liquid, just use what the boxed mix calls for).

... but with that being said, depending on how detailed you're trying to make the frog, I might not use cake for all of it. For the main body, sure, but for the legs, you may want to consider using marshmallow & rice cereal treats. You need to shape it while it's still warm, but it'll then hold it's shape once it's cooled (wear gloves, sugar burns suck). You can also carve it after it's cooled, if necessary.

If you want to use a boxed cake mix, add a cup of sour cream, an extra egg and a small box of instant pudding to your mix. You can also increase oil in the cake to 1/2 cup. This makes the cake more dense (more like a pound cake) for stacking and carving. Pound cake is a great option when carving.