Pretty much the only reason a traveller is likely to end up in Pieksämäki in the first place is that it's a major train junction where the Jyväskylä-Joensuu and Kouvola-Kuopio lines meet. The town can thus be reached by direct train from virtually all of Finland's main cities: Helsinki (4 hrs), Tampere (2 hrs) and Turku (3 hrs).
It's under 500 meters on foot from Pieksämäki railway station to the market square.
If you have half an hour or more to kill at Pieksämäki, make your way to the market (signposted as Tori), where in summer you'll find vendors of berries, freshly cooked vendace (muikku), and more. There's also a large S-Market supermarket right next to the market.