You can enter the first three letters of names and email addresses in the recipients text field and Evolution will present you with a list of matches from your address books.

To enable autocompletion, go to EditPreferencesContactsAutocompletion and choose the address books from the list that Evolution should look in for matches.

Select Always show address of the autocompleted contact to also show the email address along with the name. This can be helpful to distinguish if a contact has several email addresses.

Alternately, you can click the To:, Cc:, or Bcc: buttons to get a list of the email addresses in your contacts. Select addresses and click the arrow buttons to move them into the appropriate address columns.