A common way to build a story map is with post-it notes. It's an excellent way to engage stakeholders and the team and gives everyone a voice. It's usually a pretty good starting point for any story map.
If your team are co-located and you have wall space, you can leave your story map as post-its for the duration of the project and this can work well. But, a story map needs to grow, shrink, change, breathe — so make sure you have a decent wall space where you can constantly re-visit and re-evaluate your story map.
Inclusive for stakeholders and team
Requires substantial space
Hard to move stuff around (especially when it's in the middle of the map)
Have to re-write if you need the data elsewhere
You can also create your story map digitally. For this approach, you need a tool that allows you to create the same journey, step and story hierarchy that you can easily create with post-its. The nice thing about a digital story map is the ability to move journeys, steps and stories whilst the story map adjusts automatically.
Simple to move things around
Ability to integrate with other tools keeping the data synced
Simple to share / collaborate — no more photos of the map!
Can feel less inclusive, as often one person "drives"
Some people "freeze" at the keyboard when typing in front of a group
Ideally, using both techniques is the best option. Post-its can be used during the initial brainstorming session. Stakeholders can contribute and the team can scribble. Whilst this is happening, someone can be the dedicated digital scribe. Their job is to type up the journeys, steps and stories into the digital tool. Once the initial brainstorming has finished, the product owner and team can use the digital story map to continue onto development.