What line of work are you in?
Firstly, you'll need to secure a job - you can do a search using online job portals or have a look at the classified in local newspapers if you can get hold of some. Once you have a job, you can apply for a work permit, but this needs to be done before entering Zambia. You'll need to have a copy of the employment contract to apply for the permit. You can check out this page for more info on the job market in Zambia, and for more on visas see this page.
If possible, it might be ideal to enter Zambia on a single entry visa, do the job search, then leave the country to do the work permit application before returning.
For more info, you might also find the website for the Zambia Department of Immigration useful.