Jackson-Medgar Wiley Evers International Airport (JAN), about ten miles east of downtown in Pearl, is the main entry point. It is a small regional airport with direct flights from Atlanta, Charlotte, Dallas, Houston, and a handful of other hubs. A taxi or rideshare to downtown costs around $25; there is no rail or rapid transit link.
Amtrak's City of New Orleans line stops at the Union Station downtown, running once daily in each direction between Chicago and New Orleans. It is a slow but pleasant way to arrive if you have the time.
By road, Jackson sits at the intersection of Interstates 20 and 55 and is an easy day's drive from Memphis (3 hours), New Orleans (3 hours), or Birmingham (4 hours).