"Did you see Mr Sandi today?" This refers to a "closed" or finished time period. We would say this in the evening, or perhaps at the end of the working day. We would understand that the day is now over, or that there is now no longer any possibility of seeing Mr Sandi today. "Have you seen Mr Sandi today?" This refers to an "open" or unfinished time period. We would say this during the daytime. Even if you haven't seen Mr Sandi yet, there is still a chance that you will see him today. In other words, the situation could change.

I'd like to add to what has already been said. Though we don't normally use the terms "open\close time periods" in Russian, and I'd suggest leaving it until later, there are, fortunately, certain cases of using Present Perfect. Thus, you can use it: 1) to describe an action that happened in unstated time in the past (especially, if you can count those actions or see the result): "I've washed the car (you see, it's clean now)" or "I've been to Italy twice" (by this time I've been there twice) 2) to describe an action that started in the past and continues up to the present moment: "I've known her for six years" 3) to describe a recently completed action: "I've just finished writing the sentence" 4) to describe personal experience or changes: "I've gained 10 pounds" or "She's changed her haircut". It may sound a bit tricky and take some time to grasp the idea but in fact it isn't that difficult. Good luck! :)

В Did you see Mr Sandi today? акцентируется факт, а в Have you seen Mr Sandi today? акцентируется результат. В русском это одно и то же предложение "Вы видели мистера Санди сегодня?"