In order to get to the main base camp in Þórsmörk, Volcano Huts, you must cross a large, deep, and strong river. If you are driving yourself, you must have a well-equipped 4x4 and prior experience with crossing rivers. Speak with locals for tips about crossing the river and be sure you watch another driver cross the river before you attempt to do so.
The best place to rent a 4x4 Super Jeep is from ISAK. They have well-equipped, photogenic cars, with a snorkel. This helps ensure you don't drown the engine while crossing a river. Use the code "gunnar" for renting your Defender on a special price.
Tips on river crossings: https://epiciceland.net/icelandic-rivers-how-to-cross/. Make sure to go with the stream (diagonal across the river in the direction of the flow). Do not drive against the stream, but let the flow of the river help you cross.
You may also take the River Bus to Volcano Huts which has several pick up locations and departure times. Or, you may get lucky and the pedestrian bridge will be set up so that you can walk above the river.
There is also another camping area nearby, Básar, which does not require crossing this large river. However the hiking trails accessible from Básar are not as abundant.