This is a really stupid question, I know. I took a graphic design class some years ago and we designed our website in Photoshop and then sliced it. I have a feeling graphic designers don't do that anymore. Update me, please? :) Thank you.
There are plenty of different ways to make a website. There's no correct way to make a website. There are countless services and different approaches to making a website.
It's going to depend on what your company specializes in
- What programs they already bought
- What they plan to do with the website
- What type of computers will be using the website. Ex: desktop only, mobile only, both, or neither?
- Is it going to be something used internally only?
- If it's not going to be used internally, then what type of customers are they anticipating?
- How important is compatibility to older operating systems and browsers?
If you are freelance here are some suggestions and things to consider when making a website in 2017
You get to make your own rules unless your customer tells you specifically what they want.
For free: If I'm making a responsive website I like bootstrap for compatibility between different device screen sizes. You can use elements you made in Photoshop or SVG elements. You can do basically anything with bootstrap with HTML and CSS. You have to be comfortable using Notepad to write the website or something free like https://www.sublimetext.com/ which is just an HTML editor that makes it easier to understand.
Have Adobe: You can also consider Muse which is more for GUI comfortable users and also makes responsive websites like bootstrap and utilizes Photoshop in many ways. Info on Muse and Photoshop. Muse lets you use Photoshop for various things for example to make buttons change to a different picture when you hover over them.
Also, Adobe's Dreamweaver is an option too if you want less hand holding as it is mostly an HTML editor. Adobe has a video to help you decide whether you should use Dreamweaver or Muse
However, if you are trying to make a light website you would not use Photoshop for everything. You would create many assets as SVG in Illustrator or another free vector program if possible, because it will load a lot faster and look a lot cleaner when scaled to different sizes. More info svg.
I build (a lot of) websits for designers. Most of them work in InDesign and deliver high quality print PDF files and an InDesign package. I think that is a pretty normal workflow nowadays. This also means I get to decide on most of the responsive stuff.
Hope it helps you!