Ansdell was born in Liverpool, Lancashire, the son of Thomas Griffiths Ansdell, a freeman who worked at the port, and Anne Jackson. His father died young and Richard was educated at The Liverpool Blue Coat school for orphans. He had a natural talent for art from an early age, and after leaving school worked for a portrait painter in Chatham in Kent, and also spent time as a sign painter in the Netherlands.
He first exhibited at the Liverpool Academy in 1835, becoming a student there the following year. His animal and rural subjects proved to be popular and he soon attracted wealthy patrons. His first exhibition at the Royal Academy, London, was in 1840, with two paintings called "Grouse shooting" and "A Galloway farm". This was followed, in 1841 by "The Earl of Sefton and party returning from hunting", in 1842 "The death of Sir William Lambton at the Battle of Marston Moor", in 1843 "The Death" and in 1844 "Mary Queen of Scots returning from the chase to Stirling Castle". He went on to exhibit pictures every year at the Academy until 1885 (149 canvases in all). In 1846 he exhibited his first picture, "A Drovers Halt" at the British Institution, London, and went on to show 30 canvases there.