Mixing a kick and an 808 is a very simple process that many find confusing. There are only a few key steps required to find the perfect balance between the two instruments. However, many find confusion because the two instruments are found in the low regions of the frequency spectrum. When these two instruments fight each other it causes lots of mud and messiness in the mix. But finding the perfect balance can be a very easy process.
The first thing I do when mixing a kick and an 808 is set the levels. I bring up the level of the 808 to where it is sitting nicely below the mix and giving the mix a nice bass foundation. I then bring up the level of the kick until it is punching through the mix and giving the impression of adding punch to the 808. After I have the levels set I move on to the EQ. The first EQ change I make is to put a lot-cut filter on the kick track. I ride the low-cut filter up to about 100-150 hz, since the 808 will primarily be in the 150 hz and below range. After this I may or may not add a high-cut filter to the 808 and pull it down to about 200 or 300 hz. Whether or not I add this high-cut filter depends on how much information the 808 has in the high frequencies. But typically, the high end information of and 808 is unnecessary and will fight other instruments in the high regions.
After my EQ changes I move to the next stage of mixing a kick with an 808. This will be the compression stage. I will typically use side-chain compression to achieve the goal I want here. I will place a compressor on the 808 track and pull down the attack to very quick and the release to fairly quick. Then I will place a compressor on the kick track. On this compressor I will have a slower attack, to allow the punch to cut through, and a quick release. The next thing I will do is send the kick to a Bus. The bus number does not matter, I will use whichever bus is available. I will turn up the signal on that bus track. Then open the compressor on the 808 track (make sure you use a compressor with a side-chain ability on the 808 track). Find the side-chain feature and then select the side-chain input as the same bus you placed the kick on. What this will do is make sure that every time the kick gives signal to the bus, the compressor on the 808 track will duck out the 808 just for a split second to allow the kick tp punch through in all its glory. Immediately after the kick signal ends, the compressor will let go off the 808 and let it rumble. Then when the next kick comes in the same thing will happen. This way the 808 is ducked down to allow the kick to punch and be heard but then as soon as the kick ends, the 808 will come back up and be dominant in the mix. The entire process will happen so quickly that the average listener will not notice but it will allow the kick and 808 to play nicely together and not fight for space.
Mixing a kick and an 808 is very easy if you use this method. It allows each instrument to have its own space for the time that it needs to punch. As a side note, I may sometimes put a limiter on my 808 track to reduce the dynamic range so that it does not eat up all the headroom in my room, and that way it will stay nice and consistent throughout the entire song. Feel free to use this method whenever you find yourself mixing a kick and an 808 and I promise you will receive much better, cleaner results than you were originally.