If the server is full you automatically join Rust's queue – your current position is shown right on the loading screen. As soon as a slot opens up, the next player gets in.
Rank priority: Players with a rank are moved forward in the queue: Premium+ > Premium > VIP+ > VIP > no rank. Within the same rank, whoever has waited longer goes first. Staff members are always at the very front. Premium+ skips the queue completely and joins right away.
Dynamic slots: The slot count adjusts automatically: if the server is at least 95 % full for 60 min in a row (or there is a queue), 50 slots are added – up to 800. If it stays below 60 % for 60 min, 50 slots are removed again, but never below 300. Currently: 300 slots.
Tip: stay on the loading screen while you wait – if you cancel the connection you lose your spot. Which rank gets which priority is also shown in the "Ranks" tab under "Compare".