After that check for the latest updates. You'll have to select a server to download from. After downloading, the update window will have the "hourglass" symbol (installing updates). Immunize and you're good to go.
To the best of my knowledge, correct with one exception (see Note #1 below).... and so on down the list and then when last check/tick disappears I presume everything is finished -there is no installation that we have to wait for.
It appears that the download, verification and installation of each of the listed downloads is independent in the respect that when the checkmark appears that individual update is complete.... when a file finishes downloading the checkboxes to the left of the name will turn to a green tick (if it turns into a red cross [or something], the download failed, ...