What is the best solution to even a basement floor?

there is self-leveling cement at the hardware store. Check it out...

It depends what you mean by uneven, and why you want it smooth. If it's wavy and it just bugs you, then a self levelling mix might be fine. But don't change the pitch or you may have real flooding problems.

If ceiling height isn't an issue, you can run 2x4 joists flat on the floor, shimming the low spots [maybe grind a high spot or two], and lay a subfloor on it. You can get info in those Time/Life style books. And the ram set you use to shoot the nails into the concrete is a gas!!

If you want to lay a floor on the concrete, or if there is a drainage problem, contact a pro. They'll let you know if it needs grinding, filling, or both. And it may be cheap as part of laying the floor.

self levelling compound is the best option, try to gt the 2 part latex floor leveller, ( looks like milk) and mix in a well ventilated area as it contains ammonia, make sure the floor you are working on is completely dust free and vacuum the floor if you can, for the best result...start in the furthest orner away from the door..mix the compound according to the instructions and spread with a plastering trowel or steel float, and work out any lumps or bubbles, don't over spread it as it will level itself..another tip i've used over the years is to get some pva adhesive and water mix ( you don't need much) and brush it into the floor before you begin so the floor and leveller bond together better, and if you are working into another area, just dip a paintbrush into the water and pva mix and brush the edge so that it feathers out and you don't get any high ridges around the edge wher you are stopping..you won't believe how easy a job it really is and take your time and don't panic, it takes a ages to set, so you will have time to do it right..enjoy!!!

if you have the headroom, build a wood floor on pressure treated joists to compensate for the uneven concrete. (this will raise your floor level about 6 inches)

If you DON'T have the headroom i'd knock out the old floor completely and pour new concrete.

talk to a contractor, that's not something that can easily be taken care of especially if it was caused by foundation problems.

I agree