Assuming you are EU residents, private health cover is no longer a requirement for residency. If your NI contributions in the UK (assuming that’s where you come from?) are up to date then you should be able to get short term reciprocal health cover in Spain. Can’t remember the form number you need to apply on but I’m sure somebody will come along with that info for you.
A popular health care provider here is Sanitas. You can get online quotes from their website. Of course other providers exist too depending on where you are going to be based.
Living and Working in Spain by David Hampshire (I think) is a useful book but do make sure you have an up to date copy as otherwise you will find things like private health cover being a requirement for residency! The laws here change frequently.