Well done for finishing your sampler!
I am not an expert but this is what I do. The others might do something different.
First, you have to make sure your threads are colorfast ( does not bleed on other colours) DMC and Anchor threads are, usually.
I put my stitching in a clean basin with lukewarm water and a tiny drop of washing-up liquid and agitate the water briefly. I let it soak 5 minutes then I empty the water and fill my bowl with lukewarm water to rinse my piece. I repeat the rinsing then gently squeeze the water out.
It is rather wet at this stage. I sandwich the stitching between 2 thick towels and press down to extract the water.
After this process, I lay a thick towel on my ironing board. I put my stitching face down on the towel and a thin cloth over it. I lower the iron ( no ironing action!) on the piece , all over and gently. It does dry quickly but I let it dry completely overnight.