We have a longer article on our garden design process (HERE), but a quick guide is as follows:
Take the brief: Come and meet with you to understand your site and your requirements (you typically do not need to pay for that meeting)
Pull together base information: Organise a measured survey of the site (to include levels if it is not flat)
Tease out what will work for you: Create suitable mood boards and outputs to tease out styles and approaches that will meet your aesthetic preferences
Show you their initial proposals: Draw up the proposed plans for discussion with you and create outputs to share
Update and re-issue these preliminary plans to reflect those discussions
Create final outputs dependent upon the needs of the project and the site- for you, your builders and other contractors as needed (including planning if required)
Liaise with whoever you need them to: On larger projects there will also typically be more people involved such as architects and other contractors with whom we will need to liaise.