How do I light up my frogs like that
Well...... as cocky as it might sound, lighting is lighting.
What I mean is this.
If the skin of the frog is wet and shiny then it's going to produce a lot of specular highlights when lit. Specularity is reduced by broadening and diffusing (scattering) the light.
If there is a lot of texture to the skin then you don't want to soften and diffuse the light too much or you'll lose all the contrast and texture and it will take on a smoother and less textured appearance.
You can strike a happy balance by using modifiers like a beauty dish with the addition of a diffusion sock. This is a very common technique that preserves contrast and detail while offering some degree of diffusion that will take the edge off and lessen specularity just enough to reduce hot spots or unwanted highlights.
Of course, if you can't get close enough to the critter then forget everything I said and just shoot with ambient light or a Speedlight.. lol.. seriously, some animals sit perfectly still and are not bothered by the proximity of humans or flash and others will split as soon as they know you want to do more than just look.