The first step to improve past the beginner's method is to learn F2L, in which, instead of solving the white corners and 2nd layer as individual steps, you solve both at the same time.
I would recommend starting to learn F2L once you can solve the cube in less than 1 minute. Until you can solve it in less than 1 minute, just keep practicing!
As you learn F2L, you may get temporarily slower. But, over the long term, it will be worth it!
To learn basic F2L, check out
this tutorial by J Perm!