A lot of modern NoSQL solution don't support ACID transactions (atomic isolated multi-key updates), but most of them support primitives which allow you to implement transactions on the application level.
If a data store supports per key linearizability and compare-and-set (document level atomicity) then it's enough to implement client-side transactions, more over you have several options to choose from:
If you need Serializable isolation level then you can follow the same algorithm which Google use for the Percolator system or Cockroach Labs for CockroachDB. I've blogged about it and create a step-by-step visualization, I hope it will help you to understand the main idea behind the algorithm.
If you expect high contention but it's fine for you to have Read Committed isolation level then please take a look on the RAMP transactions by Peter Bailis.
The third approach is to use compensating transactions also known as the saga pattern. It was described in the late 80s in the Sagas paper but became more actual with the raise of distributed systems. Please see the Applying the Saga Pattern talk for inspiration.
The list of data stores suitable for client side transactions includes Cassandra with lightweight transactions, Riak with consistent buckets, RethinkDB, ZooKeeper, Etdc, HBase, DynamoDB, MongoDB and others.
