it means "Have you been busy lately?" because there is "ka" at the end of the sentence. if there is no "ka" it will be "Saikin isogashii desu" and it means " i have been busy lately".

if there's "ka" at the end of the sentence, it's a question.

ka is the key to this. If it's there, then it's a question, if not, then it's a statement. As for the subject of the sentence (which is usually invisible), you have to work it out from the context.