"To assemble the sliders" means to put together or arrange the individual components or elements of the sliders in order to complete or prepare them for use. Full definition
Sturdy homemade buns mean you can assemble these sliders ahead of time, then pop them in the oven to warm before serving. (vegetariantimes.com)
To assemble the sliders place some of the aioli on the bottom bun, top that with a patty, then go tomato, red onion, and finally the avocado and top bun. (witandvinegar.com)
Aarons insists this dish is even better the next day, so braise the meat the day before then quickly assemble the sliders before serving. (epicurious.com)