Counting in Mandarin is very straight forward and was for me one of the easiest things to learn. If you know the numbers 1-10 its very easy to also learn the weekdays and months.
If you remember the first 10 characters it is very easy to count up to 100.
There is a very straight forward logic behind the numbers over 10. Twenty is in Mandarin for example two ten.
If you would like to say for example 15, it would be in Mandarin ten five, shí wŭ(十五). In Mandarin a number would be exactly how you would read out a number, the number ten comes first than the number five.
If you would like to say 27, it would be two ten seven, èr shí qī (二十七).
Here are a few examples: