These links should help you understand motif discovery and get examples of the algorithms.
- This link on Nature explain: how does DNA sequence motif discovery work?
- Paper on BMC bioinformatics: survey of DNA motif finding algorithms
- This paper discusses some limitations and potentials of motif discovery algorithms (2005)
I hope this helps.
Also worth checking out Biology Meets Programming: Bioinformatics for Beginners https://www.coursera.org/learn/bioinformatics which can help with learning the basics of the algorithms underpinning motif discovery.