Karesuando is at the northern end of the E45, Sweden's longest road, which runs from Gothenburg all the way to the Norwegian border above the Arctic Circle. If you are driving north through Swedish Lapland, Karesuando is quite literally where the road runs out — the E45 continues into Finland as Finnish national road 21, but the road does not carry on further north into Sweden.
The nearest airport is Kiruna, roughly 200km to the south-west. There is no train service to Karesuando. Bus services run along the E45 corridor from Gällivare and Kiruna, though they are infrequent — check current timetables with Länstrafiken Norrbotten before depending on them.
From the Finnish side, Karesuvanto is connected by road to Enontekiö and the Finnish road network. The border crossing on the bridge is open and unstaffed, as it has been since Finland joined the Schengen zone.