Go to the updated page on the Nexus (if there's an indicator next to the version number noting that there's been an update, of course), hit Download with Manager but DON'T disable the original mod. Instead, select and activate the updated version, whereupon it will ask you if you want to upgrade, which will automatically deactivate the older version.
There are distinct advantages to doing this instead of manually deactivating the older one, then activating the newer one. First off, if any meshes, textures, etc. are involved it doesn't have to add them again (unless they've been changed too), which saves you potentially-lengthy install times. In addition, if there's an installer to the mod with multiple options (e.g. AmethystDeceiver's Black Tower and Black Sacrament mod or CBBE) it will preserve the settings you have activated (e.g. if I selected the UNP version of the Black Sacrament armor, then updated that mod, it wouldn't force me to choose again). --- finally free of the weeaboo name I picked back in 2003 also I'm rarely on here