How do the cycle, ROM and RAM limits on my bot's code work?

Your bot's CPU runs a fixed number of cycles each tick (512 in the compiled leagues, 256 in assembly), at 20 ticks a second. If your code runs out of cycles, the tick ends wherever it is and carries on next tick with readings a tick old. Your compiled program must also fit the ROM (4,096 words in the compiled leagues) and its variables the RAM (1,024 words); if it doesn't, it won't compile.