Liking is made simple!
Once you've made a search, you can select the 'Like' option directly from a members profile, when viewing their profile. Click the little heart beneath their profile pictures, and wait for it to turn pink to confirm that the dog has been added to your likes. 

Shown on the Home tab of your account, are all the members profiles you have liked, and the profiles of members who have liked your profile, along with your recent looked profiles.