I pick my blooms generally in the morning. No need to soak but I do keep them either in a plastic bag (with plenty of air) in the fridge or in a small mini cooler with an ice pack on the bottom (a towel or some bubble wrap in between so the blooms don't actually touch the ice pack). Once the lei is made - if it's not to be worn right away - I mist it with a spray bottle, then store again in the ziploc bag in the fridge, in the little cooler, or - and I learned this from a fellow plumerian in California - in one of those clamshell containers that lettuce, etc. comes in.
How long your lei will last depends on many things: the quality of the blooms, the variety of the blooms, the temperature, etc etc.
Generally if it's worn for - say - an evening, and then misted again and placed in the fridge afterwards, a lei can last 2-3 days.