I have a turtle. Is it a Yellow-Bellied Slider? How do I care for it?

The images are a bit blurry. It can be difficult to keep those little guys still! It does look like a YBS. They are not native to the UK and are typically captive bred.
They are quite easy to keep. They need warm, clean water, a water heater, a basing spot with an overhead heat lamp, UVB lighting, a balanced diet consisting of animal protein and plant matter, calcium supplementation and multivitamin supplementation.
For now, keep water depth no deeper than twice the length of the shell. As it grows, you can increase water depth. Maintain water quality via filtration and regular water changes. Feed a varied diet of prey (appropriately sized feeder fish, earthworms, crickets, etc.) and fresh greens and vegetables. Use a calcium and vitamin supplement and provide UVB lighting.
You can review slider care at the link below. It is titled for Red Eared Sliders, however, Yellow Bellied Slider care is the same.

http://www.anapsid.org/reslider.html