To activate a frog's love mode, you'll need slimeballs. The easiest way to get them is from slimes! Slimes spawn in the Overworld in specific "slime chunks" below layer 40, regardless of light levels. They can also spawn in swamp biomes between layers 50 and 70 in light levels of 7 or less.
An adorable fact: Baby pandas have a chance of dropping one slimeball when sneezing.
Frogs spawn in swamp and mangrove swamp biomes, in groups of 2-5 frogs. They grow from tadpoles, and their variants are determined by the temperature of the biome the tadpole grew up in.
Frogs have three variants: temperate (orange), warm (white), and cold (green). To get different variants of the frogs, currently the best way is by bringing a bucket of tadpole to a different temperature biome and letting them grow up there.
Simply give each frog a slimeball and let the magic happen (aka love mode). One of the frogs will head towards water to lay their eggs. In the case of Minecraft, frog spawn will appear over water (similar to how lily pads or glow lichen appear).
You cannot pick up this block and there’s no collision, so you won’t have to worry about stepping on the eggs as you would with turtle eggs.
If you'd like to know more on what else was included in the Wild Update, check out this comprehensive overview!