To assign a task to another user, tap or click on the task to open it. Tap or click on "Assigned To" and choose a member from the list. If you collaborate with a lot of people in the list, you can use the search bar at the top to find the person you're looking for.
If you don't already work with them, you can invite them to join Zenkit To Do by inviting them to the list or to a folder.
Another way to assign a task to someone in the web or desktop app is to drag and drop their member icon onto the "Assigned to" field! Wherever you see their icon, e.g. in a comment on the open task, or from the member drop down menu, you can drag it!