There are usually two ways to redeem points for the non-cobranded cards.

1) Transfer the points into the airline’s program. Each issuer only partners with certain airlines though... for example, you may be able to transfer Chase points to United but not AA. Once the points have been transferred, they become miles in that airline’s program and you’d redeem them for award travel just like you would any other miles you earned with that airline. Award availability may be capacity-controlled and you’re almost not certainly going to earn miles or elite credit.

2) Redeem through the issuer’s travel portal. This is almost like buying a cash ticket at whatever the going cash price is, and then paying for it using your points, usually at a fixed rate (such as $0.01/point). You can redeem your points on pretty much any airline and don’t need to worry about award availability, because your bank basically just buys a cash ticket from their travel agent - no special partnerships are required between your bank and the airline. You can probably earn miles and elite credit for the flights, though in some cases these can be treated as special/exception fares and you earn differently than if you booked direct. The biggest downside here is the redemption rate. When you’re pegged to such a low value per point, it makes zero sense if you want to redeem for premium cabin travel... and if coach travel is what you want, you might as well just use a cash back card.