The verb "manquer" follows a different construction in French from English. And it's very confusing for students.

Tu me manques = I miss you = you are being missed by me

The solution it to slightly change your English sentence so you get the correct word order in French.
Instead of thinking I miss you, switch it to you are being missed by me. 
That will give you the correct pronoun/person to start with in French.

And that's the key.

• I miss you = you are being missed by me = TU me manques.
• You miss me = I am being missed by you = JE te manque.
• He misses us = we are being missed by him = NOUS lui manquons.
• We miss him = he is being missed by us = IL nous manque.
• They miss her = she is being missed by them = Elle leur manque.
• She misses them = they are being missed by her = Ils/Elles lui manque.

The verb has to agree with the first pronoun (the subject)

That is the second trick of "manquer". A mistake I hear all the time is: "je vous manquez". The verb "manquer" has to agree with the subject, the first pronoun - here the je. Not the vous.

• Il vous manque - not il vous manquez (you miss him)
• Tu nous manques - not tu nous manquons (we miss you)

The middle pronoun can only be me (m'), te (t'), lui, nous, vous, leur

 In this construction, "manquer" used an indirect object pronoun, and that is what this "vous" is.

• So, you're only choices for the middle pronoun is among:
• me or m' for I
• te or t' for you (of tu)
• lui both for he and she. This one is tricky to remember, watch out, no "elle", nor "la" here!

• nous for us
• vous for you (of vous)
• leur for them, both feminine and masculine. Not ils, not elles.

Manquer without pronouns

Of course, you don't have to use pronouns. You can use nouns. The logic remains the same.

I miss Camille - Camille is being missed by me - Camille me manque

Note however that if you only used nouns, not even subject pronouns, you'd have to add a "à" after manquer:

Olivier misses Camille - Camille is being missed by Olivier - Camille manque à Olivier.

The verb manquer also has other meanings

Manquer also has other meanings, and the constructions are much easier - they are the same as in English.

To miss something, as you missed a train. The construction is then just like in English.
J'ai manqué le train - I missed the train.
In colloquial French, we'd say "j'ai raté le train".

Manquer de + something means to lack something.
Ça manque de sel - it lacks salt - or in English, there is not enough salt...

Manquer de + verb means to fail to do something - but it's a very old construction, we don't use it often. You may run into it in writing, but that's about it.
Cette voiture a manqué de me renverser - this car almost ran me over.
Nowadays, we'd use faillir:
Cette voiture a failli me renverser.

Voilà, getting accustomed to using the verb manquer is going to take some practice - my 10 years old daughter who is bilingual still struggles with it - in both languages! She never knows who she should start the sentence with !! 

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