Best of all was the warm thick slobber Of frogspawn that grew like clotted water (8–9)
The speaker's excitement comes through in "best of all." It seems like only a child could get that excited about "thick slobber."
[…] Here, every spring I would fill jampotfuls of the jellied Specks to range on window-sills at home, (10–12)
Again, the speaker's enthusiasm for watching the frogspawn hatch into frogs is childlike. You can almost feel his anticipation—like a kid waiting to open his birthday presents—as he waits for it to happen.
The fattening dots burst into nimble- Swimming tadpoles. (14–15)
The big event! They "burst" open. It's a party!
[…] Miss Walls would tell us how The daddy frog was called a bullfrog And how he croaked and how the mammy frog Laid hundreds of little eggs (15–18)
You can tell the speaker's innocence by how he refers to the male frog as "daddy" and the female as "mammy." He's probably pretty young, and may even still refer to his parents as "daddy" and "mammy."
To a coarse croaking that I had not heard Before (25–26)
You get the idea that maybe our speaker hasn't heard a lot of things before. He's young, he's innocent, and chances are he has many new experiences ahead of him.
I sickened, turned, and ran. (31)
Whatever he sees—frogs mating, or just so many frogs croaking and hopping around all at once—he's not sticking around for the second act. It's too much for our speaker's innocent eyes, and it upsets him to the point of having to flee the scene.
[…] The great slime kings Were gathered there for vengeance and I knew That if I dipped my hand the spawn would clutch it. (31–33)
By the end of the poem, the speaker seems to have lost some of his innocence regarding the world, at least this little slice of the natural world. He's become wary of the frogs—now they're menacing slime kings—that he was once so unwaveringly excited about.