I did let you know over skype about the meeting.
Is the above statement correct? How can I make sure there is a difference between present and past tenses of "to let"?
This isn't as confusing as you think to a native speaker of English, but it depends on what you want to say exactly.
I let you know over Skype about the meeting.
I would assume this is past tense, first and foremost because simple present tense is not used very often in English unless you are expressing habitual activities (e.g. I usually let people know about meetings over Skype) or narrating someone's action. Present progressive is typically preferred to express "this activity is happening right now" or that something is about to happen immediately.
Context also helps here. If a meeting is happening now and you are telling me you let (in the past) me know about it (I'm guessing maybe I forgot about the meeting?), obviously you are referring to the past.
Now, if you said this, to tell me that you are about to let me know over Skype about the meeting (maybe we are talking in person about the meeting and you want to follow up on Skype), it will sound ungrammatical. You want to say I am letting you know or I will let you know.
Perhaps you are a bit angry with me that I forgot about the meeting. Emphatic tenses serve to make expressions stronger, thus:
I did let you know over Skype about the meeting
is fine, but keep in mind it has an emphatic mood to it.