Generally the owners will give the sitter a key, show them the location of a hidden key, or provide access via a garage door opener or keypad. They should show you ahead of time the location of any items you will need while you are caring for their home/pets, and it's a good idea to ask them about any other needs you might have while they are there, like clarifying whether you are allowed to use their restroom or where cleaning supplies are located should you need them. If you're staying for overnights or anything longer than drop in visits, also clarify if there are areas of the home you should avoid and what they are comfortable with you using (like TV, kitchen supplies, where you should sleep, etc). If any other questions come up during the stay, message the clients to clarify; showing the owners you care about their privacy and comfort will help put them at ease and prevent any disputes. Sending lots of pictures can also help reassure a nervous owner, since they'll see how much you care about their pets.
If you get a weird vibe from someone, like they don't trust anyone in their space, it may be in your best interest to decline the stay if you aren't able to reassure their fears. There will always be some risk when working in another's home, but I think for the most part, if you're doing a good job and being respectful of your clients' spaces, problems are unlikely.