Counting is a very basic skill and it's usually something students learn the first week. However, just knowing the numbers doesn't really mean that you can count in Chinese. To be able to use numbers in Chinese, especially large ones, you also need to practice a lot.
Let's go through the learning process together:
1. Learn the basic numbers
2. Start using the numbers
3. Learn to handle large numbers
Learn the basic numbers
Numbers in Chinese are ridiculously logical, so learning them isn't very hard. In order to be able to count to 9999, you only need to know 13 syllables! Knowing numbers is also of great practical value, so you should try to get good at them as soon as possible. They also give you lots of opportunities to practice tones, both in isolation and in words.
Here are the basic numbers:
Combining the numbers is easy. For the numbers 11-20, just add 十 (shí) in front of the numbers 1-9. For the numbers 20-99, add the right number of tens in front of each, so 21 is 二十一 (èrshíyī) and so on. The same goes for all the numbers up to 9999, except you also need to add the right number of hundreds and thousands, of course. Unlike in English, when the number contains a zero you have to read it out, so 101 is 一百零一 (yìbǎilíngyī).
If there are many zeroes in a row, such as in 1001, you only need to say one of them.
Start using the numbers
One reason numbers are harder than most students think is that it's one thing to be able to recall a sequence of numbers and quite another to be able to use numbers freely. In other words, counting to ten in any language is very easy, but being able to read random numbers is much harder.
Here are some ways of practising:
Count backwards, count with skip or both at once
Practise reading and writing down phone numbers
Generate random numbers in a spreadsheet program
Practise with number-intense topics, such as dates
Learn to handle large numbers
Large numbers in Chinese are quite difficult to learn to a level where they feel completely intuitive. The reason is that while we in English have new words for every set of three zeroes (thousand, million, billion), Chinese has new words for every set of four.
You normally only need these two words since the numbers become very big beyond this, but the problem doesn't lie in learning the words, but converting between languages quickly. Often, the only safe way is to count the number of zeroes. I've found that the best way of learning these large numbers is to connect them to a phrase that makes intuitive sense, such as learning to say that Chine has 1,3 billion people (十三亿).