잇다 means to join or to connect, and 있다 means to exist, so they have different meanings, but the only difference in their pronunciations is that 잇다 is pronounced with a long vowel sound, and 있다 with a short one. In other words, the 이 in 잇다 is pronounced longer than the 이 in 있다.
Korean-English dictionaries do not usually mark short and long vowel sounds, but many Korean-Korean dictionaries do, which is a good reason to also consult a Korean-Korean dictionary when learning a new word. Korean-Korean dictionaries usually leave a short-vowel sound unmarked but mark a long-vowel sound with a colon after the vowel sound. For example, 있다 is listed as "있다," and 잇다 as "잇:다" in many Korean-Korean dictionaries. That means 있다 is pronounced /읻따/, and 잇다 is pronounced similar to /이읻따/.
But do long-vowel sounds really make that big a difference when speaking Korean? Well, except for the 을 and 에, the only other way to distinguish the following two sentences in spoken Korean is by using the short-vowel sound in the sentence with 있는 and the long-vowel sound in the sentence with 잇는.
- 남과 북에 있는 [인는] 다리
a bridge between the North and the South
- 남과 북을 잇는 [인:는] 다리
a bridge connecting the North and the South