Cut the existing coupler or nozzle from the end of the hose with a utility knife or sharp scissors. Make a clean, even cut. A jagged or crooked edge will lead to leaks. If the end of the hose is ragged or damaged, consider making the cut further back from the end to remove the damaged portion of hose.
Attach a compression fitting to the end of the hose. Compression fittings vary in terms of installation methods, but most require a male end on the fitting slid inside the hose.
Tighten down the compression fitting on the hose end. Ensure you have enough hose fed into the fitting then hand-tighten the nut on the compression fitting as snugly as you can.
Test the hose fitting for leaks. Run the hose with an adjustable nozzle attached. Turn the nozzle off so that no water sprays from the end of the hose but the house spigot is still on. This puts the hose under pressure and will be the surest way to find any leaks. Tighten down the compression fitting nut, as necessary, until no water emerges from the fitting.