Wrap yourself in plastic:
well, this is only a partial solution as donning waterproof gear doesn't keep front tire splatter from hitting your face and all that street crud getting flung onto your bike components.
Last month I went into the garage to check on my fendered bike and remembered it's on spring/summer/semi-permanent loan to a friend. I fiddled with the various fender parts and pieces, but wasn't able to get them to fit on the Redline or Vaya. I might've been able to get them to work with some cutting and filing, but didn't have the motivation. I should after today's steady drizzle and more in the forecast. But most likely I'll just put it off because dry summer weather is just around the corner. I hope.