There is the possibility of creating a responsive website without using a framework, but using them will make your life easier and consequently save time by having several things "ready". I do not recommend using if you are a beginner, I believe that eliminates a phase of learning.
I developed projects with several frameworks among them, Bootstrap, Foundation, Semantic Ui and currently do not use because the code is not always well organized, I do not use so many classes and the semantics used is horrible.
A cool tip is to read some Mobile First, Media Queries, Relative Measures. Do not use gambiarras in the project, the organization in the initial stage will help you a lot in the course of the same.
[...] it would be easier [...]. In general it is easier not to reinvent things ready, not to try to attack problems already solved. A very easy way is to use Bootstrap in LESS -- you can create your own grid in very few lines and reuse everything that is already ready.
– Bruno Reis
The best I’ve seen is http://ink.sapo.pt/ Int Interface Kit, where you can easily configure your website shapes according to the average device screen size, using only CSS and open source JS.
– Please_Dont_Bully_Me_SO_Lords