Most manufacturers provide the option to update the BIOS online. That is, the CMOS is reprogrammed directly via the Internet. But this is not advisable as it carries more risk than offline flashing. Any interruption in your connection to their website could seriously corrupt the BIOS, perhaps even making it impossible to start your computer.
In general, the mobo manufacturer will have a downloadable file for making a bootable floppy disk. The floppy carries the updated BIOS data. You boot with the floppy and carry out the instructions.
If for any reason the flashing process does not complete properly, do NOT turn off the computer. If you turn it off, the BIOS will probably get corrupted. Just repeat the flashing process.
Carefully read the manufacturer's instructions. It's not a good idea to make a big jump in the BIOS version. E.g., if your BIOS is v1.0 and the manufacturer has v1.2, 1.5 and 2.0, flashing may not be successful if you jump straight to 2.0. Follow the manufacturer's recommendations.
Also, there are often variants of the same basic model. E.g., a manufacturer may have motherboard models ABCD-X and ABCD-Y. These two models may have different BIOS'es that are not compatible with each other. Use only the update file intended for your specific model.