The trick that works best is using a smaller bottle or an airtight decanter instead of leaving the wine in the original one with air inside. If you've got a smaller glass bottle, pour what's left and seal it up tight; that way you minimize the oxygen in contact with the liquid. In the fridge it'll last quite a bit longer like that, like a week or even a bit more if the cork is decent.
About your Rioja from three days ago: if the bottle was poorly sealed in the fridge, it's probably already a bit off. Red wine doesn't last as long as white once it's open, and without an airtight seal the oxidation process speeds up. I'd say just taste it directly: if it smells like acetone or vinegar, toss it. If it smells good and tastes normal, go for it.
There's another homemade trick that works for a lot of people: stick a marble or glass ball in the bottle before you cap it. It takes up space and reduces some of the air, though honestly the best method is still pouring it into a smaller container or using those vacuum stoppers that are cheap and effective. The fridge is mandatory anyway - without that nothing lasts.