It's easy to make the best sauces and gravies. Basically the ratio for a medium sauce is:
2 T. Butter or Fat
2 T. Flour
1 Cup Liquid

Use 1 less T. Flour for a thinner sauce, and 1 extra for a thicker sauce.

Always melt the butter first, remove from heat and sift in the flour.
Whisk vigorously until well blended and smooth.
Return to heat and gradually add the liquid stirring to incorporate.
Keep stirring and heating until thickened.
Keep warm on lowest heat until ready to serve, as the cooling process thickens it more
Add salt and pepper at the end to get rid of the flour flavor.

When adding onion or mushrooms to the sauce or gravy, add it to the melted butter and sauté, before completing the rest of the recipe'.

When making a white sauce, use milk or cream.
When making gravy use stock, bullion, or both.

When making a gravy in a dish during its cooking process, sift flour into a bit of cold liquid and whisk vigorously, before whisking into the pan to avoid lumps.

Basic White Sauce
2 T. Butter
2 T. Flour
1/4 t. Salt
1 Cup Milk, Cream, or Stock
Melt Butter in a sauce pan.
Remove from heat and whisk in Flour until smooth.
Return to low/med. heat and add Liquid slowly while stirring, until smooth and thickened.
Raise heat if you need to quicken the thickening process.
Stir constantly.
Finish by adding the Salt & Pepper to cover the flour flavor.