Set up a ladder in the basement below the floor where you have the linoleum installed.
Pinpoint the source of the squeak by having another person step on the spot to make it squeak. You should see a slight gap between the subfloor and the top of the floor joist.
Apply wood glue to the face of a thin wood shim. Slide the shim into the gap, breaking it off for size if necessary. Slide another shim in from the other side of the joist if it is difficult to push the first shim through -- don't force it. Have your helper step on the floor again. Add another or a thicker shim if the squeak is still present.
Squeeze construction adhesive into a gap that is too narrow or too long for a shim. Apply the adhesive on both sides of the joist. Work the glue into the gap with a plastic knife. Allow the adhesive to dry. The adhesive fills the gap while preventing the two wood surfaces from rubbing against each other.
Measure the distance between the two joists that surround a squeaky spot caused by the ends of two pieces of subfloor rubbing together. When a seam falls at a point perpendicular to joists and is not well supported from beneath, the boards can move, causing a squeak. Cut a length of 2-by-8 lumber to fit tightly in the space between the joists. Apply construction adhesive along three edges -- the top and both ends -- and push the lumber between the joists and up against the bottom of the subfloor so it spans the seam between the two pieces. Let it dry.