Advanced Select List custom field behaves the same way as any other custom field. While browsing your JIRA project issues just note, that the custom fields are by default added to the end of the Details section of your issue. You will probably find all the newly added custom fields here.
Custom field section at the issue detail
To edit the issue:
Browse to the issue, where you want to change your Advanced Select List value.
Locate your custom field and move mouse pointer over it. The pen icon appears next to the value field.
Click the pen icon to enable the value field for editing.