Semey is in eastern Kazakhstan, roughly 700 km northeast of Almaty and 1,000 km east of Nur-Sultan (Astana). It is not on the main tourist circuit, and getting there takes some commitment — which is part of the point.
By air — Semey Airport (IATA: PLX) has regular domestic flights from Almaty and Nur-Sultan. Flight time from Almaty is around 90 minutes. Air Astana and SCAT Airlines both serve the route; book ahead as flights fill up.
By train — The train from Almaty is the most atmospheric option, passing through the southern Kazakh steppe before climbing into the more varied landscapes of the east. Journey time is around 24 hours. A train also connects Semey with Nur-Sultan (roughly 18 hours). Overnight services with kupe (compartment) berths are comfortable enough for the journey. The train station is on the south side of the river, a short taxi ride from the centre.
By road — Buses and shared taxis run from Ust-Kamenogorsk (Oskemen), three to four hours to the east, which has its own airport if you want to approach from that direction. The road from Almaty via Karaganda is long (around 12 hours) and best avoided unless you are travelling overland for the experience.