Sytist is a very robust system with a lot of features. It can be used as an entire website or just an addition to your website for selling photos, booking calendar, project proofing and all the other feautres.
To use just in addition to your existing website, here is how you want to set it up.
1) If hosting and installing yourself on your existing website, install in a sub folder. It will be link yourwebsite.com/some-folder. some-folder would be the name of the folder you install it in.
2) Site Content -> Create New Section. In the new section wizard select Client Galleries and create that section. That is where you will create galleries. You can also create a booking calendar section, project proofing, etc...
3) Go to Site Content -> Mange Home Page. Click Featured Content and select the section you created for your client photos. This will display the galleries on your Sytist home page. It will basically look like this,
You can also click the more options link, scroll down and check the option to add the find my photos form on the home page so clients can enter their gallery password if needed.