I just cut a mall branch off with some buds and put it in a pot 3/4 full of dirt, put a little bit of fertilizer on it then fill the rest with dirt and watered it. Will I need to use rooting hormone on it or will it work fine but take awhile to grow roots?
Lilacs can be grown from cuttings, but is much easier to dig a small sucker from the bottom of the plant. It should have some roots attached to it along with some soil and you can pot that up and be much farther ahead in the same amount of time. It is best to do this before the new growth is started, but you can still dig it and try to transplant a small sucker to where you want it, if it has already begun to grow. (My neighbor came and got some from me a couple of weeks ago and they looked fine the last time I saw them and they had some new growth on them already when she took them. To make a cutting you need new soft growth, not the woody stem from last year, you would need to dip it in rooting hormone and keep it in a humid environment, such as a mist bed. and use bottom heat, also. A plastic bag kept snuggly over your cutting and misted with a spry bottle several times a day, should also suffice. The cutting should always be kept moist this way, don't let the foliage become dry. You will want to keep this out of direct sun, also. Watch closely, it may take a couple of weeks to see if it roots. You will need to use sterile soiless mix, not a potting soil to stick your cuttings in. Unfortunately, I don't think your method will yield the results you are looking for so you might want to try this again.
Lilac is a multi-branching shrub. It naturally send out roots that erupt as a volunteer. Very much like rhizomes of grass do. This smaller satellite branch is easy to divide and take as a miniature clone of the parent. Lilac also set viable seed. Lilac if you are a little handy should be propagated with either semi hardwood or hardwood cuttings set in a terrarium. Most propagators use 1/2 sharp (pool filter) silica sand, with 1/2 peat, and rooting hormone on the base (cut) of scion. I've not needed to try propagating lilac because divisions are to easy to take.
I rooted a small Lilac cutting under glass in early spring a couple years ago. I took the cutting from the soft new growth on the bush, and kept it in an east-facing window until it rooted in 3-4 weeks, I misted it every now and then but kept it under the glass to lock in moisure until it started growing. I believe I used a softwood rooting hormone powder. : )
I have dug lilac sprouts at the sides of my bushes most times of the year, but I would not recommend during the summer heat. They already had roots and were easy to move to a new location. They are all doing nicely. Forsythias can be stuck right into the ground and will root if kept wet until they start growing again. I use new wood for this. Those will also root if a branch is kept close to the ground, similar to raspberries. I have forsythias and lilacs right next to each other in my garden.
I've never had any luck starting from cuttings :'( I've had pretty good luck digging up the side shoots that they send out I'd think if you dug up a "sucker shoot" you be very successful, especially in your climate!