Curves present two challenges. First, the inside rail will end up longer than the outside. Second, a kink can easily develop where two curved sections join as the track tries to spring back to a straight shape.
The first challenge, uneven rails, can be remedied easily with a pair of rail nippers. These special flush-cut pliers are available at hobby shops and are specially designed to give a smooth cut in model rail. Don't use them on wire or other products.
Arrange the track section so the loose rail is on the inside of the curve. Bend the track to shape and the rail will extend beyond the last tie. Nip the inside rail off even with the outside rail with the nippers. Spike the track, leaving the last 3 to 6 inches loose if the curve will continue through the joint.
Soldering can be intimidating at first, but it is essential to smooth track. To prevent a kink at the joint, join the next section while the joints are straight. Apply a small amount of solder flux to the rails and solder both together at the joint. Using flux and working quickly, you can solder the rail without melting ties. File off any excess solder.
Now continue bending the curve through the joint and on to the next. You can further improve your curves with easements and super elevation.