Go to Setup  and click on the Object Manager tab.  This will give you access to any object, whether standard or custom:

Select your object, and then choose "Fields & Relationships" to get the field list and find the field you are looking for.

Go to Setup / App Setup / Create / Objects.

There you'll see a list of all the custom objects in Salesforce.

To examine and edit the fields for any of these objects, click on the hyperlink for the object name.  

(Note: Clicking on edit will allow you to edit some parameters of the custom object, but not the fields of the object itself).

In this case we want to edit fields associated with Volunteer Opportunity so we click on the words "Volunteer Opportunity"

1.  Objects that are part of the HandsOn Connect package are not FULLY editable.  You can only edit characteristics that won't break the application for future upgrades.

2.  Custom Object Definition Detail shows some of the characteristics about the object itself.

3.  Standard Fields are fields that salesforce automatically adds to any custom object.

4.  Most of the fields in a custom object are custom fields.  So it's here we look for the field we are trying to modify:  

We can see that Program Area (Local) is a picklist field.   The field type is always indicated in the "Data Type" column.

Click on the hyperlink for the field to get to the field detail.

in the field detail screen, you'll see a list of the current picklist values.

You can click on NEW to add new values, (or can reorder or replace the existing values).  Let's click on NEW

You can add as many additional values as you want to the list and when you click save they will be added to the possible picklist values.  Click Save.

Click on reorder to determine the order they appear in the list.

Use the up and down arrow keys to move a selected item up or down in the list to determine the order.

You can also opt to have the values appear alphabetically.

Use the "Default Value" picklist to choose which item should appear by default in the picklist if you want something other than a 'null' value.

Click Save.

You can delete any item on the picklist by clicking on the DEL link.   However,  any records already using that value will still retain that picklist value.

(Deleting will prevent any NEW records from using that value - but old records will retain it until edited.)

Instead, you might want to FIRST replace the value of records that are using that existing picklist value.

You do this by clicking on the Replace button.

Use the Replace button on the picklist values list to remove an existing picklist item or rename it.

Put in the exact spelling of the item you wish to remove from the picklist, and then select the item you wish to replace it with.  

So in this case we're assigning the value to "none".

If I had created a new value named "Neighborhood Safety" -- I would add that first -- and then change "Neighborhood Watch" to Neighborhood Safety!

Click Replace.

Having made the replacement - you can now feel safe about deleting the "Neighborhood Watch" item from the picklist by clicking DEL.

You'll get a confirmation message that the picklist values have been changed and replaced.

Scroll down on the object you're editing and see if it has record types assigned to it.   If it does -- you'll need to also set the picklists for each listed record type.  (Different record types can use different picklist values :-)

Go to Record Types in the object - and define which of the picklist values for the field you've edited, are available for each record type.  Don't forget that even 'contact' has a record type.  So always make sure the record type picklist is updated after you've added picklist values to the field itself!

See this post for information on setting picklist values for different record types.