I've heard that writers often have several agents in their careers. My first book did not sell, and though I do not blame my agent for that, part of me thinks it might be time to part ways. How would a writer go about doing that? Would the agent take it personally? If a writer's contract says they have to give 60 days notice before ending the agreement, how quickly after giving their written notice can a writer begin searching for new representation (for a new book the previous agent has not put on submission)?
If you want to part ways with your agent you send her a certified letter saying so (if that's what the contract calls for, and most of them do.)
And most reputable agents won't discuss representation with you until after you've parted ways with Agent #1.
As to whether an agent takes it personally, it doesn't matter. It's not a personal relationship, it's a business relationship. Sure I regret losing some clients more than others, but I've remained cordial with 95% of my former clients.
You need to be aware of the fact that authors who have already had an agent have a higher hurdle at the query stage than those who haven't. I always ask what went wrong, and what they're now looking for. "My book didn't sell but I don't blame her for that" would be a huge red flag to me.
I notice that you don't actually have any specific problems with your agent, just a general sense that you can do better. That would also be a huge red flag to me since you've demonstrated you'll decamp even if I'm doing my job well. That bodes poorly for the investment you want me to make in your career.
Be careful about thinking you can just get another agent and things will improve. This is utterly unrealistic.