Both words translate to “always” in English, but their meanings are slightly different.
언제나 has more of a meaning of something that is continuous; there is not a time when it is not happening.
Ex. 그녀가 언제나 예뻐요. She is always pretty.
항상 has more of a meaning of something that happens repeatedly.
Ex. 항상 도서관에서 공부해요. I always study in the library.
Tag: all the time

늘 = Always (usual)
부모는 늘 자식 걱정을 한다 = Parents always worry about their children.
늘 먹는 걸로 주세요 = I’ll have the usual.
늘 만나던 곳에서 만나자 = Let’s meet at the usual place.
당신의 친절을 늘 기억할게요 = I’’ll always remember your kindness.
그는 아침에는 늘 기분이 좋지 않다 = He is always in a bad mood in the morning.
안경을 늘 쓰세요? = Do you always wear glasses?
늘 허름한 옷을 입는다 = She always wears shabby clothes.
너 늘 이렇게 긴장해 있니? = You always this nervous?
Frequency

항상 – Always
맨날 – lit. everyday, always, all the time
항상 물어보고 싶었어요 – I’ve always wanted to ask you
중국어를 맨날 공부하는데, 아직 어려워요 – I study Chinese all the time, but it’s still difficult
보통 – Usual/Usually
~(으)ㄹ 땐, 때는 – usually/ past tense used to
저는 학교 갈때는 항상 자전거를 타고 가요 – I usually ride a bike when I go to school
한국에 있을 때는 외식을 많이 했지만, 일본에서는 집에서 자주 밥을 만들어 먹어요 – I used to eat out frequently in Korea but in Japan, I usually make my own meal at home.“
자주 – often
가끔/가끔식 – sometimes
보통 기차 여행 – the usual train trip
한국 영화 자주 봐요 – I watch Korean movies OFTEN
자주 한국 영화 봐요 – I watch KOREAN MOVIES often
가끔 서점에 가요 – I sometimes go the BOOKSTORE
서점에 가끔 가요 – I SOMETIMES go to the bookstore
negation (~지 않다)
별로 – hardly/barely
전혀 – never
거의 – almost not at all
저는 축구를 별로 좋아하지 않아요 – I barely like soccer
요즘에는 운동을 별로 안 해요 – These days, I seldom work out
시간이 없어서, 친구들을 거의 못 만나요 – I don’t have time, so I can hardly meet my friends