I have recently beem forced to make many fiber gaskets that are on the heat exchanger of a Detroit Diesel boat motor.
I have always resisted making my own gaskets because I never had the proper materials, tools or they just tend to look tacky.
On my current project I really have no choice.
McMaster-carr has a very large selection of gasket materials. I have found the burna-n and organic material in 1/64" and 1/32" to cut well and being rubber based it is very flexible. It resists oil and water so is a good universal gasket material.
Cut a piece of material larger than you need.
Use the flange you are making the gasket for as a hole template.
Use the drill press on a high speed to drill the holes. At high speed the material drills without tearing.
Get a good supply of exato blades they dull easily when using a flange for a template.
The magic trick is a small wood carving set. It will have radius tools, 90 degree, amd straight tools to trim corners and enlarge cutouts.
I am using a small wood carving set from Wal-Mart. Carving tools are in the arts and crafts area for $3.98.
Cut on a chopping block from the kitchen. The white plastic blocks are soft enough to protect the tools.
I also have found that a magnifing light is a nice to have.
Keep your tools sharp and be careful.

With developed skill and patience you will never be stuck begging for a gasket again.