There are several border crossing points.
From the Polish direction: Mamonovo, Bagrationovsk and Gusev.
From the Lithuanian direction: Sovyetsk and Morskoye (on the Curonian Spit).
You will need Russian visa. Even if you have one it may take days to get in by car. It is probably quicker to fly to Moscow and then fly or get a train to Kaliningrad.
The Most Frequently Asked Travel Questions about Kaliningrad Oblast
Where To Stay & Best Hotels in Kaliningrad Oblast - updated Apr 2024
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Kaliningrad Oblast Travel Guide from Wikitravel. Many thanks to all Wikitravel contributors. Text is available under Creative Commons Attribution-ShareAlike 3.0, images are available under various licenses, see each image for details.