Incremental Deploy module is built on top of Deploy module. The latter must already be installed on a site before Incremental Deploy is installed. This is because Incremental Deploy makes a couple of changes to the database table that holds information about the items in a deployment plan. Incremental Deploy is not actively supported, or updated since 2011.
This documentation assumes your source and destination sites are already set up as per the Deploy documentation here.
On your source site, install Incremental Deploy module (requires Settings Audit Log). If you are using Nodequeues and would like to be able to deploy their contents, install Nodequeue Deploy module. Likewise with flag_deploy and nodewords_deploy modules, if you want to deploy global flags and meta tags respectively.
On your destination site, install Incremental Deploy Service module and, if deploying nodequeues, flags or nodewords, Incremental Deploy Services Extra module.
On the source site, go to Site Configuration -> Incremental Deploy Configuration and you will see two config settings. The first controls the number of items that are displayed per page in the listing of changed items to be deployed. The second is for making sure certain variables never show up in the active deployment plan. Many variables are strictly environment-specific and should never get deployed to the target environment - examples are the internal variables used by Incremental Deploy module itself, which are prefixed with incdeploy_ and are added to this configuration setting by default.
After adding / editing some nodes on the source site, navigate to Site Building -> Incremental Deploy. Here you will see a list of the changes you have made. There may be some unwanted items in that plan, for example you may notice some variables showing up that should never get deployed. In this case, select those items and hit "Block selected". This will remove those items from the active plan and ensure that they won't show up again. If you simply want to remove some items for the plan but don't mind if they show up again the next time they change, select them and hit "Delete selected". Of the remaining items, you may still not wish to deploy all of them right away. Simply select the items you do wish to deploy and hit "Deploy selected". This will take you to the same screen you are used with deploy module where it asks you to select a target server. You will notice, however that it now shows you a summary of what you are about to deploy. Continue as you would with a regular deployment, entering your credentials for the target server, and submit. From this point on, everything is more or less the same as with a normal plan, but when you view the log for the deployment, you will notice that the very last item is something you did not add to the plan: Post Deploy Tasks. This gets added automatically to all Incremental Deploy plans and all that it does is invoke a hook on the target environment that allows other modules to act on the fact that a deployment has just completed.