23pieces

I learned how to count numbers today. ( 1つ, 2つ...)
But my textbooks only show 1-10. How about 23pieces? Do we say にじゅうさんつ？

The つ ending only works on cardinal numbers up to (and including) 9.
From 10 onward, the つ drops off. It can be replaced by the "counter" for the item it is that you are counting, or just -ko (個) if you need a generic "counter".
So 23 would be にじゅうさんこ.