The first thing you can do is read the label on the herbicide you used thoroughly. You should have done that before you used it but I digress; if you at least followed the application instructions correctly you shouldn't have done any damage. Over-application of herbicide, even one with biodegradable chemicals, can "poison" the soil and prevent anything from growing in it, good or bad.
Most herbicide blends, whether "selective" or "ground-clearing" (usually determining whether they kill only broadleaf plants or grass as well), contain a chemical designed to prevent germination of new seeds. These chemicals are not selective (the way they work, they can't be), and will prevent your grass seed from sprouting. The instructions on the herbicide will tell you how long to wait before seeding treated areas, or treating newly-seeded areas. Usually this is one to two months either way.
Once that time has passed, ground prep is usually as simple as loosening the top inch or so of soil with a bow rake. A full-size roto-tiller, designed to churn up several inches of soil for gardening, is usually not necessary unless the ground is REALLY hard or REALLY rocky. However, a "cultivator" may be called for; these are tools with a set of offset spinning spikes that do a combination of ground fluffing, thatching, weed-eating etc. These come in powered and unpowered variants and are generally easy enough to handle even on slopes, but can have trouble with rocky soil.
With the ground prepped, most seeding products are as simple as loading them into the spreader, setting the desired dispersion rate, and heading out. However, you must then keep the ground nice and moist. Zoysia is very drought-tolerant, but like all grasses the seeds need plenty of water to grow and establish quickly. Watering once or twice a day for about 30 minutes, or long enough to keep the ground wet down to about 3 inches but not enough to turn it into mud, is the way to go. I would generally advise on a sprinkler instead of soaker hose, because a sprinkler will have less of a footprint and so you can leave it in the area between waterings without ending up with a twisted snaking bare path where the hose was. Grass generally takes about 2 to 3 weeks to take hold in an area, and can take up to a full season to really cover the ground well and "dig in" to prevent erosion. As was stated, Zoysia takes longer to establish than other grasses, so be patient. Once the grass is about 2" tall you can start mowing it, but you should still water regularly (at least every other day) until the turf is at the desired thickness.