The particle -에 is the locative particle. -에 describes the static location of where a place or object exists (-에 있어요.)
-에 also indicates the destination or goal when used with directional verbs such as 가다 or 오다. 집에 가요. (Go home.)
But then there is -에서. This particle indicates the location of an action. 학교에서 공부해요. (Study at school.) With this particle, the -에 can be omitted, usually when following a vowel. 어디에서 공부해요? can be 어디서 공부해요? (Where do you study?)
So -에 is a static location. Where something "is" or is going.
-에서 (or -서) is where something "happens."
Proper examples of "~에서" include:
"오늘 학교에서 싸웠어" (Today I fought at school)
"집에서 낮잠을 잤어요" (I took a nap at home)
"어디에서 왔어요?" (Where did you come from?)
"미국에서 왔어요." (I came from America)
"중국에서 중국어를 배웠어요" (I learned Chinese in China)
Proper examples of "~에" include:
"지금 사무실에 있어" (I'm at the office right now)
"내일 우리 집에 오세요 (Tomorrow, come over to my house)
"어디에 갔다왔어?" (Where did you go [just now]/[on vacation]?)
"호주에 갔다왔어" (I went to [and came back from] Australia)
"어디에 살아요?" (Where do you live?)
"한국에 살고있어" ([Right now] I live in Korea [but it's just temporary])
"어제 현대백화점에 갔어" (Yesterday, I went to [the] Hyundai Department Store)
"책상위에 열쇠 있어" (The keys are on my desk)
"창문 앞에 있어" (It's in front of the window)
"서울에 사람이 많아" (There are a lot of people in Seoul)
"지금 형이 집에 없다고?" (Did you say that your brother is not home right now?)
"집에 가" (Go home)
cf.
"집에 왔어요" (I'm home [while talking on the phone to your wife])
"집에서 왔어요" (I am a citizen of a place "HOME"; lit. I come from home)