Examine the shelf in the armoire. If the shelf is stationary, you will have to replace it. The shelf should lift off the "L" brackets it is resting on. If it doesn't lift off, locate the screws that are holding it in place and unscrew them, then lift off the shelf. Unscrew the screws from the L brackets and discard the brackets. You now have an empty space to work with. Save the shelf itself for reuse.
Purchase two slides for sliding shelves. Most hardware stores have these, but you may have to look in the kitchen remodeling department, because these slides are commonly used in kitchens. They come in pairs, so purchase one set. Most come with a package of screws to use in installation.
Attach the two slides to the armoire at the height you will want the new shelf to be. This should be toward the lower area of the opening, so the sewing machine will not sit too high for comfortable use. Attach one end of each slide -- the end closest to you as you face the armoire. Raise the back end of one slide until it looks approximately level. Then place a level on the slide and make adjustments until the slide is perfectly level. Screw the back end in place, then tighten the screw that is in the front end. Leveling will keep the sewing machine from sliding out of the armoire unexpectedly. Repeat the process for the second slide.
Attach a shelf to the slides. If possible, use the old shelf you removed. It that is too thick to put screws through, use a board cut to the same size. Your shelf should be approximately 1/2 inch thick to give it enough strength to hold the sewing machine while still allowing you to place screws through it. Screw the shelf to the slides. The slides will have pre-drilled holes to accept the screws, so line up your screw through the shelf into each slide.
Place the sewing machine on the shelf and test the slide-out feature. You should be able to pull the sewing machine toward you easily with one hand.