Newborough is famous (at least locally) for its red squirrels. It isn’t too unusual to see them when walking in the forest. Usually you will actually hear them before you see them: hear their sharp little nails scratching on the tree bark as they scamper away. If you scratch your own nails against the bark, you’ll get an idea of the sound to listen out for.
However, it is unusual for me to either have a camera with me and / or to be able to capture a half-decent photograph of one of our red squirrels. Here’s one of a baby who was too scared to move away. The other is a bit of a cheat as it shows a squirrel in one of the compounds in the forest.
(nb that compound is no longer here – it’s quite an old photograph)
If you are visiting and want a good chance of seeing one of the squirrels, the Llyn Parc Mawr car park and picnic area is worth a try (OS GR SH414669). The squirrels (and birds) are fed there and have become quite confident. It’s best to go early as they make themselves scarce if the car park becomes busy. The Forestry Commission’s information sheet is available here (pdf) which shows the car parks and forest trails etc.