Changing a contact from organization to individual (either One-to-One or Individual Bucket)
For example, let's say that Jane Dolman has left The Amazing Foundation. She has history with your organization, so you don't want to delete her record, but you want to be sure she is no longer directly connected to The Amazing Foundation.
Simply delete the Account Name from her contact record and Save the record.
You'll find a few things have happened automatically.
The contact will either be added to the Individual Account or a One-to-One contact will be created as specified in Contact Settings.
If Household Settings are such that every Individual contact gets a Household, a Household record will be created even if one didn't exist before.
You'll also find that an Affiliation record has been created connecting Jane to her now-former association with The Amazing Foundation. You can edit this record to adjust the Start and End dates as appropriate.
Changing a contact from individual (either One-to-One or Individual Bucket) to Organization
Let's say Jane now works at The Even Better Foundation and she is now the organization's primary contact there. It may make sense to associate her directly with the Foundation rather than continue treating her solely as an individual.
The account she's moving to must already exist in Salesforce. Simply edit the Account name on the contact record to move her from the old individual account to the new one and Save the record.
Going forward, any gift created off of Jane's record will be credited to The Even Better Foundation. However, any of Jane's previous gifts are still linked to her personally and not to The Even Better Foundation, as her original account (either Jane Dolman or Individual) still exists.