How to control Java heap size (memory) allocation (xmx, xms)

Java memory FAQ: How do I control the amount of memory my Java program uses (i.e., Java RAM usage)?

One of the Linux servers that I use is a little starved for memory, but I need to run a Java program on it periodically to run some utility tasks. However, every time I try to run the program I get this Java heap size error message:

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