Smudging specifically refers to burning herbs in sort of a ritualistic fashion. A really well-known one is burning sage, but you could use other herbs too (just check to make sure they are safe to burn first).
It really depends what you want to use it for though. Sage is often used as part of cleansings or protection work. Some can be used to increase spell potency, or to assist in spellwork in other ways. Some can be used to heighten focus during spellwork.Incense is actually a form of smudging since incense is just a combination of ground up herbs mized with a specific type of binding agent (which can also be an herb).
So part of this is asking yourself what you want to accomplish first.
A great resource are the articles Herbs A-Z in the articles tab on this site. I use those and Ctrl + F to search for specific properties in herbs sometimes.
Another part of smudging is going to come down to how you choose to perform the ritual. You can simply burn as incense or burn regular herbs in a similar fashion. You can kind of move a clump through the air to spread the smoke. If I use sage during a cleansing, I will usually move it around doorways and windows since cleansings are about clearing negative energy from a space, and personally I think outlining entrances/exits to the space keep it "clean" of that energy for longer. But it all depends on what you're working on and how you see feel it should be done.
What i would add is that when you smudge move counterclockwise (widdershins) to banish and clockwise to attract. You can walk in those directions or move your arm/hand as you hold the smudging component.
There is some great advice already listed above. I would like to add a smudging can be a burning herb, wood, or resin however, in addition as smudging can also be a water based spray or mist one uses to cleanse a specific area or objects. A smudging essentially cleanses the negative energy from an area, scared space, or the objects that are passed through the smoke or mist. This is done in a ritualistic fashion often combining sound vibrations in the form of chanting, signing, or the playing of instruments. I often smudge my home with the help of my essential oil diffusers, as I can no longer burn sage or other resins and woods for cleansing purposes inside my home. I still use these combustible items in open and well ventilated spaces outside, but I have found the mist is better for this practitioner while within my scared abode. However one chooses to smudge or what items they use to smudge with, one thing remains the same which is the intention to remove old negative energy and clear space for the new positive energy one draws.
