For me, the easiest solution is not to arrive in a village with no beds left. Sounds funny, but it usually works.
How to achieve that? That's what I do:
a) Walk distances that allow me to still continue a bit further if necessary (I want to be able to add another 5-10km at the end of the day). So should there not be a bed in the town I wanted to stop in, I can still walk to the next one.
Since that's not always possible, other solutions are:
b) Stop midday or for a second breakfast in a town with a walk-in or "no reservations possible" albergue with high capacity / lots of accommodation. Ask myself, do I want to walk further today, or do I need a half/short/rest day? If I'm very tired I can just check into the albergue (first come - first served, so no problem if I arrive early). If I want to continue and walk a longer day,
c) Check that the next town is still within my preferred walking distance and that there are several albergues there, so that the likeliness of getting a bed there is high.
d) Check if shortly after that town (<5km), there's another albergue, just in case, or
e) If I want to be absolutely sure to have a bed in the village I intent to walk to, call and ask how busy they are and if possible make a reservation. This is a good solution especially if you want to walk a very long day and arrive late, if you know you'll be too exhausted to walk further to the next albergue/village, or if the village where you want to stop has only few beds and the next place is far away.
f) If all fails, walk into a bar, have a nice drink, find out where the next place with a bed is, and get a taxi there.
g) Sometimes when talking to the locals or hospitaleros of the places that are 'completo', beds suddenly appear from nowhere ;-)
h) bring a light foam mat and a decent sleeping bag. If there's only room on the floor of a sports gym or fire station or in the albergue garden / on their terrace ect., that will be helpful. Add a tarp or tent and you also have campsites as extra option for accommodation (there are a few official ones, with warm showers and all).
That has always worked for me so far.
There's lot of panic regarding beds. Personally I've always found place to sleep so far, and most of the time I do not make reservations.
Unpopular opinion, but for me it's mostly online hysteria, mainly created by people looking for bookable private rooms, places that will accept luggage service, people who are set on staying in a certain town/place, walking until exhaustion to places that are known to have a limited number of beds without plan b), ect.
Many will disagree with that statement, but after four times walking the Francés with not really witnessing the famous bed race, and more often than not finding a bed in the first albergue I walk into, I start to believe it's mainly a myth ;-)
I haven't walked in september so far, though, I have to say. Maybe that's the secret!
Overall, if you don't walk in april/may, and not in september, if you're fine with dormitorios or a mattress on the floor, you'll most likely have good chances of always finding a place to sleep without too much stress. June is a nice month to start walking for example.
I've had to sleep outside of an albergue once, but that was not because there were no beds. I'd found a sick kitten and most places would not let me in because of that. So that doesn't count, I'd say! I still was allowed by the owner of the albergue to put up my tent in the garden or sleep on the bench in front of the albergue, and had a nice dinner at that place. So it was still a good experience!
So. Keep in mind that sometimes you might need plan b-h) to find a bed, but usually there is one, and no need to panic. No need to run, no need to be afraid.
Happy planning and Buen Camino!