Is this usual way to say something "tastes good," or is there another common way?
For example, in English and German, we can say both: "the egg is yummy" ("tasty" isn't really said but is recognized)/"das Ei ist lecker" and "the egg tastes good"/"das Ei schmeckt gut" (or just "das Ei schmeckt").
We also use "dobrze smakuje" (I wouldn't rather say "smakuje dobrze" in this case but it is correct of course). "To jajko dobrze smakuje" (This egg tastes good). "Dobrze" might be replaced by "świetnie" (great). We may also say "smakuje komuś"/"komuś smakuje" ("komuś" should be replaced by a proper pronoun): "To jajko mi smakuje" (This egg tastes good to me).
"When I became a man I put away childish things, including the fear of childishness and the desire to be very grown up." - CS Lewis
I left nursery school 19 years ago and I say "yummy" quite often, but to each their own.
Can I also say "To jajko to smaczny" ? Or is it more common to say "To jajko jest smaczne" because double "to" in the sentence will sound weird?
You can't. Firstly, as "jajko" is neuter (that's why you use "to", which is the neuter form of "this"), the adjective also has to match: "smaczne".
Secondly, you can only use the construction with "to" if on its both sides you have noun phrases. Here, on the right side you have only an adjective, so you can't use this construction.
As for double "to", it sounds perfectly possible, even if a little bit weird. "To zwierzę to tygrys" (This animal is a tiger). A normal sentence.
It's very confusing that "to" can be a verb and the neutral "this" at the same time.
It can be used as a copula (thing A = thing B, or thing A belongs to the category of thigs B's), as in "tygrys to kot." Copulas are considered verbs in grammars that don't have the concept of "copula." :)