还 is largely smilarly to the english "still" or "yet another", and used like a conjuction as "and".
usually, when you want to express one or more options/things in a sentence you use "还 something".
Note: the other meaning of 还 is as a verb to mean "return", "giving back (something)"
有 is "have" or "to exist"
是 is "to be", "is/are/am.."
therefore, 还有 is "still exist (another)...", "and there is another...", "and also..."
eg. dogs 还有 cats have four legs.
"dogs, and also cats have four legs"
eg. he 还是 not here
"he still is not here"
eg. he STILL hasn't reached AND (still) he is at home!
"he 还是 not here, he 还在 home!"
"他还没到,他还在家!"
In the chinese version, there the AND emphasis is already expressed in 还
Notice that it would be more straight forward to use "dogs 和 cats have four legs". Hence, in colloquial situation, 还有 is used mostly when you start a sentence... then half way you want to add more content or you remember yet another something, then you use 还有.
eg. "When you reach home, please remember to eat.. oh, and feed the cat"
When you reach home, please remember to eat.. oh, 还有 feed the cat.
another standard phrase 还是, as a conjuction, would mean "or" and have the same colloquial function. If right from the start all options for "or" was known, 或 would be used instead.
e.g. A or B, please choose == A 或 B, please choose.
e.g. so you are thinking of A... or is it B? == so you are thinking of A ... 还是 B?