FIRST: What script do you ultimately want to go for?
SECOND: Is it naturalistic? If so, then the process involves evolving the writing system over time.

So, say I want to make a naturalistic alphabet.
1. It starts with drawing up pictograms and logograms, keeping the writing medium of the culture in mind.
2. Have those glyphs change as writing media change; perhaps if this writing system was loaned from another culture, think of ways how that could've changed the overall aesthetic of the writing system.
3. Then, determine when in the language's history does the writing system occur (especially if the writing system was loaned).
4. Next, determine how frequently the culture updates their spelling. This will have an impact on the spelling rules the culture would have to contend with. Writing systems tend to have more inertia to change compared to the spoken language. So the earlier the introduction of writing, the more that spelling reforms come into question.

As you go through each of these steps, make sure you document it as thoroughly as you can. In the end, you should have a set of spelling rules for your orthography

AS FOR THE ACTUAL DESIGN AND AESTHETIC OF THE ORTHOGRAPHY
My tried and true method is to look for inspiration in natural and constructed orthographies, note some features and aesthetics I'd like to have expressed in my system, and applying some basic design principles as I realize the concepts.

Some of those design principles are: properties of the medium, shape language, gestalt principles like proximity and continuity, and more depending what I need to keep in mind as I design the glyphs.

As I've always mentioned when it comes to world building, and thus conlanging for a con-culture: ask A LOT of questions. Where did the writing system come from? What direction is it going? How many people in this culture are able to read and write? Should the spelling be easy or hard? Etc.

I can only answer some much. If you want more resources, you can watch Biblaridion and Artifexian for some resources.