How to clean vinyl records

One of many simple and cheap ways to do it is to get a flat pan deep enough and large enough to submerge a record.  Get also a soft brush, preferably one that is designed for LP brushing.  There several choices out there.  Fill the pan with tap water plus a bit of Dawn dishwashing detergent.  (Dawn has been blessed by the vinyl cognoscenti.)  Soak the LP in this for a minute or two then brush it down with your brush.  Then rinse the LP in pure tap water, and let it sit vertically to dry or dry it with a cloth that does not leave a thready deposit.  Then open a nice chianti.

Would it matter if I opened the Chianti before the process ? :-) what about the label in the middle, would that be at risk of pealing off ? 

You will definitely run into an issue with the label if it is uncoated or not fully adhered.  Even coated labels don't particularly like getting wet.  At a minimum, it will almost certainly spot.

My personal preference has always been an old-school style record brush with a good cleaning fluid for records in very good to excellent condition already.  Moldy records and records with greasy fingerprints can be handled with a dedicated brush and isopropyl alcohol or Dawn.  I've never needed to submerge any, but there are also things like the Spin Clean that submerge the unlabeled portion.

I suggest you do an archive search here on cleaning records.  There are as many techniques as there are forum participants in 50 or more threads, and one of them is sure to seem feasible for you.

Good luck & happy listening!