You can access the advanced filtering screen in the Contacts view via tapping on the filter icon. There you can choose to filter the contact list by type of contact (i.e. Totalview contact, personal contact or favourite), or by custom field (e.g. capability, division, title, etc.).
Note that when having multiple selected items in one filter group (e.g. Capabilities), it will filter using an OR operator, meaning that it will find people with either one of these properties. When selecting multiple items across filter groups (e.g. Capabilities and Divisions) it will use an AND operator, meaning it will find people that match the criteria for all those groups (while respecting the OR conditions within one filter group).
In order to quickly turn the the advanced filter on or off, you can use the toggle on the right side.
You can search for any person in your contacts by typing a phrase into the search field at the top. Note that searching will be carried out in the currently filtered group only. In order to search in all contacts, you need to disable your filters first.