Breakdown of Jeg kigger på et andet skilt.
jeg
I
et
a / an (neuter)
på
on / at / in (a language) / of (after nouns like end or start)
skiltet
the sign
Questions & Answers about Jeg kigger på et andet skilt.
Why is it andet here instead of anden?
Because the word for sign is a neuter noun (et skilt). The word for other or another has to match the gender of the noun it describes. Since we have et, we use the neuter form andet. If it were a common-gender noun like a car (en bil), you would use en anden bil.
Why do we need på here? Doesn't kigger already mean looking?
kigger just means the general action of looking. If you want to say you are looking at an object, you must add the preposition på. So, kigger på is the fixed phrase for looking at.
Does et andet skilt mean a different sign, or one more sign?
It can actually mean both, just like the English word another! Context usually makes it clear whether you are looking at a completely different sign, or a second sign in addition to the first one.
How would I change this sentence to say I am looking at other signs in the plural?
You would drop the article et, change the adjective to the plural form andre, and make the noun plural (skilte). The sentence becomes: Jeg kigger på andre skilte.