Every gene can have a tag attached to it which prevents the gene from being used to create RNA (the tag is a methyl group, so this is called "methylation"). Since the RNA would then be used as instructions for creating a protein molecule, inactivating a gene by tagging it generally causes the cell to stop producing particular proteins. Since each protein has one or more specific jobs to do in the cell, this causes the behavior of the cell to change. There are a huge number of known proteins (millions maybe? I don't actually know), and a vast potential number of proteins (if you just consider all possible ways of arranging the 20 amino acids into a chain), so there are a vast number of ways that cell behavior can change over time. Indeed, this is how we manage to have different types of tissues at all, including our very complicated immune system with cells that act autonomously to protect against disease.

Also, it's well established that there are plenty of feedback loops here. An active gene can code for the production of a protein that activates or inactivates other genes. There are numerous pathways by which external stimuli can amplify or inhibit all of these feedback loops, so external conditions often result in changes to which genes are tagged.

As you can imagine, the state-space of all of this is immense; far larger than just the number and type of genes that you have. Mapping it all is a vast project that might easily take thousands of years.