The simplest and most effective way of propagating this plant is to use stem cuttings. The cuttings should be softwood, which is the part of the stem that is not the newest or the oldest growth. Knowing which part of your plant is the softwood is often the hardest part of the propagation. The best time of year to take a cutting from the smoke bush is during the summer in June, July, or sometimes late August. The way to tell if your stem is ready is to bend it. If the stem bends without breaking, it is still too soon. If the stem doesnt bend, then you have waited too long. If the stem breaks with a characteristic snapping sound, then those are the cuttings you should take. You want to avoid taking cuttings that are excessively thin or thick. This is because thicker cuttings root slowly or not at all, and thinner cuttings usually will not survive. The best time of day to take the cuttings is early in the day when the shoots are fully hydrated, and the sun is not yet at its hottest. After taking the cuttings, it is important to keep them cool and moist until you are ready to plant them. This can be accomplished easily by placing them into a container with damp paper towels. Lateral shoots generally make the best cuttings. Your cuttings should be three to five inches long, and you should make your cut just below a leaf node. After taking your cuttings, prepare them by removing the lower leafs and wounding them. Wounding is accomplished by stripping half an inch to an inch of bark off the bottom of the cutting. Next, the cuttings need to be covered in root hormone. The important thing is to make sure the wounds on the stem are completely covered. Never dip your cuttings directly into your container of root hormone, because it is possible that you will contaminate it. Instead, empty the amount you think you will need into a smaller container and use that. Get rid of the leftover hormone (don't put it back into the main container). Now you're ready to plant the cuttings. You will want to use a growing medium that has good drainage, because excess moisture can cause your cuttings to rot. It is often a good idea to cut any remaining leaves on the stem in half, shown below. This is to cut down on transpiration loss because the leaves are still performing photosynthesis even though there are no roots. If you have the facilities for it, bottom heating and misting will encourage root formation. If you don't, controlling the humidity can be accomplished on a small scale. Do this by placing stakes in the corner of your container, and cover the plants with plastic, as shown below. These pictures were taken from a website about stem cutting propagation and are not actually smoke bush, but the procedures are the same. Keep your cuttings well watered, and continue to check them each week for roots. Within a few weeks, your cuttings should be ready for transfer to a larger pot, and eventually to an outside garden.
Another common way of propagating this deciduous shrub is by splitting the rootball. This is accomplished by digging up the entire shrub, and evenly pulling apart the roots into multiple parts. Then all that needs to be done is replanting them. This is used less than stem cuttings however, because of the difficulty involved in digging up the shrub and manually pulling it apart.
The other way of propagating this shrub is simply by growing it from the seed. The reason this technique is less utilized is because of the time it takes. Sometimes it can take up to two years before you see any growth. To do this, start by overcoming seed dormancy. This is done by placing the seed in a thermos with hot water, and letting it soak for twenty four hours. Once the seed is completely dry, it is ready to be planted. The best time to do this is in the spring, after all possibility of frost has passed. Pick a place that recieves a generous amount of sunlight, and place the seed three eighths to half an inch into the soil. Because it takes such a long to germinate, mark the place where you planted the seed so you don't forget. Keep the soil moist during germination, but be sure to use a fine mist setting on your hose. If you don't, you may actually wash away the seed because it is so small. If you are planting more than one, place them about a foot apart so that they have adequate room to grow.
Propagation from tissue culture is not generally done, simply because propagation by other methods is much simpler and cost effective.
References: 1. http://www.finegardening.com/how-to/articles/propagate-your-shrubs-from-softwood-cuttings.aspx
3. Propagating deciduous and evergreen shrubs, trees, and vines with stem cuttings by F. E, Larson, W. E. Guse, Pacific Northwest Cooperative Extension