Step 1: Backup 
\Steam\SteamApps\common\Stardew Valley\Content\Animals\cat.xnb
and
\Steam\SteamApps\common\Stardew Valley\Content\Animals\dog.xnb

Step 2: Unzip the mod file and place cat.xnb and dog.xnb into \Steam\SteamApps\common\Stardew Valley\Content\Animals

That's it!