´dükkana giderse bir litre kola alsın´

I know that almak means to buy and here it means if he goes to the market tell him to buy a lıtre of cola...

but why did we say alsın? Ä° mean alsın ıs for ´you´ and not ´him´ and where is the translation of ask him...

we have written -> order form of the verb + ´you´ ending..

so how we say tell them to come early?

Yes, it´s tricky. There are places you use -sin for the second person

gel-ir-sin = you come

But not in this case. Pay attention it´s right after the verb stem

gel-sin = let him come, tell him to come, I demand/order him to come

For the second person it would just be a bare verb stem (like in English)

gel = come

"alsın" in you first sentence means ´let him buy´, it is a third person (he/she/it) imperative (giving instruction) suffix.

Your ´Teach yourself Turkish´ book has explanations if you look up

-sin in the rear index (it is on page 105 in my copy)

Click here for further reading

This form is also used in the very common Turkish expressions

GeçmiÅŸ olsun - May it pass (said to people who are sick, or have problems)

Kolay gelsin - May it come easy (said to people who are doing work)

To tell someone to come

Gel! (You) come!

Gelsin! (her/him) = let him/her/it come!

Geliniz! (plural you-more polite,formal)

Gelsinler! (they) = let them come!

thank you very much