It works like this. A typical sizing is 4 slots in a bucket, with 2 bucket choices. So your first choice, you arrive at a bucket, and it is just a linear array of length 4. You can put your element anywhere! After a while, when you go to insert into your first choice and you find all 4 slots taken, then you can take ANY of those and try to put it in its alternate bucket. If that alternate bucket is full, you evict from that bucket, too! Thanks to the random nature of your hash functions, it works out very well. 2 bucket 4 slot gets you near 95% occupancy without many evictions on insert.
When you go to lookup, you check your first bucket, and you check all 4 elements until you find it. If you don't find it, you go to your alternate bucket and check all 4 elements. But that's it - only two random accesses (the 4 slots will easily fit in a cache line). It's not so bad to check all 4 elements because the cost is really dominated by loading the line to begin with.
I really recommend a read of some of the cuckoo papers, it's cool stuff.