This work was done in vitro, meaning it's "test tube" work, not clinical work.
There are many ways to analyze blood cells, flow cytometry various kinds of staining, and "sandwich" assays of various types, ELISA, ECL, and (now rarely used) RIA. PBMC cells, "white blood cells" can be manually separated using a particular technique using a reagent called "Ficol." There are now very sophisticated means for separation, magnetic beads, etc, and instruments, such as those made by Miltenyi Biotech.
The authors here used a technique known as "AIM," "activation induced marker," which involves activating the cell and looking for molecules produced by the cells, "markers," most often small proteins.
They activated the cells giving immunity by spiking them with peptides - fragments of the viral proteins" - and when cells were activated, this proved there is an immune response.
On a technical level, here is a paper that describes the AIM assay, a research tool: A Cytokine-Independent Approach To Identify Antigen-Specific Human Germinal Center T Follicular Helper Cells and Rare Antigen-Specific CD4+ T Cells in Blood
These kinds of tools have been around for a long time. When I was a kid I used to make RIA kits, and I'm an old man.
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