Learn Swedish: Jag ser dig.

In Swedish, a few very common short words are pronounced differently from how they are spelled. Dig is almost always pronounced like the English word day (or dej in Swedish spelling). The same rule applies to mig (me), which is pronounced like may.

Why use dig here instead of du?

Du is the subject pronoun, used when 'you' are doing the action (as in 'You see'). In this sentence, 'you' is the object receiving the action ('I see you'), so you must use the object pronoun dig.

If I am talking to a group of people and want to say 'I see you', do I still use dig?

No, dig is only used when you are talking to one person (singular 'you'). If you are talking to two or more people, you need the plural object pronoun er instead: Jag ser er.

Does the verb ser change depending on who is doing the seeing?

Nope! Swedish verbs do not change based on the subject. Whether it is jag ser (I see), hon ser (she sees), or de ser (they see), the present tense verb stays exactly the same.