CD8+ T cells are generated in the thymus and express the T-cell receptor.It can also be found on natural killer cells, cortical thymocytes, and dendritic cells.It recognizes peptides presented by MHC Class I molecules, found on all nucleated cells.These cells are very important for immune defence against intracellular pathogens, including viruses and bacteria, and for tumour surveillance.
Your question appears simple but there are several answers depending on the species (human vs mouse) and the state of the CD8 T cell activation.
Naive CD8+ T cells express CD62L (L-selectin) integrin, IL-7Ra (CD127), S1PR1 and CCR7 chemokine receptors.
They also express the costimulatory molecule CD28 and negative regulators of T cell activation such as TGFbRI and VISTA. These are all surface markers but they also express specific transcription factors such as Foxo-1 and KLF-2
Just after activation and during priming, CD8 T cells upregulate the expression of CTLA-4 and CD69 then later PD-1, and LAG-3 as well as Fas. As the CD8 T cells are primed for cytotoxic potential, they express Granzyme B (GzmB) and Perforin.
CD44 is an excellent marker for antigen experience of mouse T cells.
However, human CD8 T cells are different since naive cells are CD45RA+ CD45RO- while effector T cells are CD45RO+ CD45RA-
However, there are many more molecules than those I just listed. For a more comprehensive knowledge of these, please refer to these resources:
1-https://www.nature.com/articles/ni.2590
2-ImmGen is also a terrific resource where you can check for the expression of specific markers
4-Article Comprehensive Phenotyping of T Cells Using Flow Cytometry: P...
There is one minor, yet important point to consider. The classically defined CD8+ T cell subset is the αβ CD8 T cell. However, there are also αα CD8 T cells which are part of intraepithelial T cells in the intestines.These cells do not express the β TCR subunit and their role in gut homeostasis remains unclear.