I am new to administraton in Appian, but I hear there is a way to move a process

If by process you meant a process model, you can add the process model to an application, export it and the import it to the new environment. Please check the following documentation:
forum.appian.com/.../Importing_and_Exporting_Applications
If you meant moving all your running processes to a new Appian version, you need to do a migration. Please check the following documentation about Migrating to the latest version:
forum.appian.com/.../Migration_Guide.html

What I need to do is mograte a process instance to the latest version deployed in the environment. The new version has a new sail rule that needs 6 parameters instead of the 5 that used to be passed. If I could migrate the instance to tha latest version deployed, I could soulve the probelm.

Is this SAIL form the only piece you wish to change in the older running process(es)? How many running instances are you dealing with?

two active instances are running. I need to migrate the 20 or so active to the new form call. I guess I could edit those instances to call the old form, but if there is a way to migrate them to the new, that would be a bit easier for me.

Here is the documentation. Based on the use case and number of instances, I would think editing those instances is the better solution than process upgrade.

forum.appian.com/.../Process_Upgrade_Planning.html
forum.appian.com/.../Process_Upgrade.html

After looking at the documentation I agree with you. Thanks for your help, it has been very useful!