Well... generally the first step would be to consult with your prescriber. (You probably didn't need me to tell you that.) Typically what you'll do is to taper ("titrate") down off of whatever it is you're taking now & begin taking (& gradually increasing the dosage of) the new antidepressant you'll be taking... both at the same time I would expect... at least that's been my experience.

It is true that not every antidepressant works for everyone. Plus AD's can poop out over time. So sometimes it is necessary to consider a change if the AD you're taking isn't getting the job done. Here's a link to an article, from PC's archives, that talks about talking to your doctor regarding a med. change:

How to Talk to Your Doctor About Changing Your Meds