This is a method I used to create one of my conscripts. It was inspired by Hangul (Korean). I used all 26 letters from the English alphabet, then did 0 - 9, and some punctuation. That came to more than 777 letters and characters that I had to make up for it, so, unless you're up to that, I recommend you choose fewer letters to use.
ONE: PICK THE LETTERS AND/OR SOUNDS YOU ARE GOING TO USE
For this example, I will only be using vowels, but you'll want to use all or some of the letters/sounds from your own conlang.
TWO: MAKE A LETTER FOR EACH OF YOUR SOUNDS/LETTERS
Pretty straight-forward. This is just like in Alphabetic and Phonetic.
THREE: MAKE COMBINATION LETTERS
Make a chart with your letters going across the top, and across the bottom.
And then fill in the empty spaces so that there are letters that represent the combined letters. For example, the first empty box will be for AA, the second (going across) will be EA, then IA, etc. The second row starts with AE, EE, IE, etc.
And that's it! You can do punctuation and stuff if you want to too.