Tissue fitting is one way of checking the fit of your pattern before working up the final garment. It can be an alternative to (or used in addition to creating a muslin). If you choose to tissue fit in addition to making a muslin, you'll want to tissue fit first, then use the adjusted pattern to create your muslin.
While tissue fitting is certainly a quicker process than creating a muslin, you will probably find that the fitting results are not as exact. For extremely tailored pieces, you'll want to work from a muslin or combine tissue fitting with creating a muslin. Also keep in mind that the tissue paper is not likely to behave the same way as your fabric, particularly if you are working with fabric that has a bit of a stretch to it (fortunately, those garments will be a bit more forgiving anyway). Whichever method or methods you use, fitting before creating the garment in your final fabric can save you quite a bit time, frustration and wasted effort.
The basic idea behind tissue fitting is that you pin or tape the pattern pieces together and then check the fit of the pattern on your body (while only wearing close fitting garments, like a cami and leggings, or only the undergarments you plan to wear with the final garment), noting any areas that need adjustment-- maybe the length is too long or too short, or the waist isn't matching up with yours.
If you want to try tissue fitting, be sure to enlist a sewing buddy to help you; the process can be a little bit tricky if you don't have an extra pair of hands.
Cut out and press your pattern pieces with an iron. It's important to work out any creases or wrinkles in the pattern since they will affect how the tissue will fit. Unless you have a general idea of what size you'll need, it's a good idea to cut out the largest pattern size along the cutting line, that way you won't have to re-grade the pattern if you do end up needing the larger size. Tape or pin them together to assemble one half of the garment. Make sure you are pinning along whatever the seam allowance is noted as in the pattern. Most people are fairly symmetrical, so unless you have special fit issues, you can get away with only mocking up half of the garment. Any adjustments will be made on both sides. If your left side does vary from your right side, you'll want to mock-up the full garment to make proper adjustments.
You will probably find it helpful to use a marker to indicate areas that need to be adjusted directly on the pattern.
Once you're done, you can begin cutting your fabric from your adjusted pattern. While you might still need to make minor adjustments during or after sewing, the tissue fitting process should resolve major issues before you begin cutting into your fabric. For more help with fitting check out Angela Wolf's Craftsy class Tailoring Ready-to-Wear and achieve a custom fit with all your clothing. Or learn more about getting the right fit for petite sewing.
Have you tried tissue fitting before? Let me know in the comments how it worked out for you!