If something is independent of the number of elements, like this = that, it is O(1)

In a simple loop, like

for(int i = 0; i<n i++){ this = new thing(); }

I simply look at the number of times the loop will be executed in terms of n, i.e. O(n)

or maybe it was like:

for(int i = 0; i<n i += .5){ this = new thing(); }

then it would loop thru 2n times, which as n tends to infinity, becomes basically O(n)

but I cannot figure out how to solve the ones that are nlogn, or log base 2 n, o2 2^n etc.

Can anyone provide an algorithm for assessing the algorithms?