Such a strategy depends on the flavour of cloud you have chosen (IaaS, PaaS, SaaS, BaaS) and might require to adjust the way you on-board in the first place. Let me shed some light on the options:
IaaSWhen renting virtual machines from a book seller, a complete box from classic hosting provider or a mix of bare metal and virtual boxes from IBM, the machine part is easy: can you copy the VM image over the network (SSH, HTTPS, SFTP) to a new location? When you have a bare metal box, that won't work (there isn't a VM after all), so you need a classic "move everything inside" strategy.
If you drank the Docker cool aid, the task might be just be broken down into managable junks, thanks to the containers. Be aware: Docker welds you to a choice of host operating systems (and Windows isn't currently on the host list).
There are secondary considerations: how easy is it, to switch the value-added services like: DNS, CDN, Management console etc. on/off or to another vendor?
It get a little more complicated when you look at the services.
First look at persistence: is your data stored in a vendor propriety database? If yes, you probably can export it, but need to switch to a different database when switching cloud vendors. This means you need to alter your code and retest (but you do that with CI anyway?). So before your jump onto DocumentDB or DynamoDB (which run in a single vendor's PaaS only), you might want to checkout MongoDB, CouchDB (and its commercial siblings Cloudant or Couchbase) , Redis or OrientDB, all of them run in multiple vendor environments.
The same applies to SQL databases and blob stores. This is not a recommendation for a specific technology (SQL vs. NoSQL or Vendor A vs. Vendor B), but an aspect you must consider in your cloud strategy.
The next check point are the services you use. Here you have to distinguish between common services, that are offered by multiple cloud vendors: DNS, auto scaling, messaging (MQ and eMail) etc. and services specific to one vendor (like IBM's Watson).
Taking a stand " If a service isn't offered by multiple vendors, we won't use it" can help you avoid a lock-in and will ensure that you stifle your innovation too. After all, you use a service, not for the sake of the service, but to solve a business problem and to innovate.
The more sensible approach would be to check if you can limit your exposure to a vendor to that special services only, should you decide to move on. This gives you the breathing space to then look for alternatives. Adding a market watch to see how alternatives might evolve improves your hedging.
Services are the " Damned if you do, damned if you don't" area of PaaS. All vendors scramble to provide top performance and availability for the common platform and distinction in the services on top of that.
After all one big plus of the PaaS environment are the services that enable " composable businesses" - and save you the headache to code them yourself. IMHO the best risk mitigation, and incidentally state of the art, is a sound API management a.k.a Microservices.
Once you are there, you will learn, that a classic Monolithic Architecture isn't cloud native (Those architectures survive inside of Virtual Machines) - but that's a story for another time.
SaaSHere you deal with applications like IBM Connections Cloud S1, Google Apps for Work, Microsoft Office 365, Salesforce, SAP SaaS but also Slack, Basecamp, Github and gazillions more.
Some of them (e.g. eMail or documents) have open standard or industry dominating formats. Here you need to make sure, you get the data out in that format. I like the way Google is approaching this task. They offer Google Takeout, that tries to stick to standard formats and offers all data, any time for export.
Other have at least machine readable formats like CSV, JSON, XML. The nice challenge: getting data out is only half the task. Is your new destination capable of taking them back in?
BaaSIn a business process as a service (BaaS) the same considerations as the SaaS environment come to play: can I export data in a machine-readable, preferably industry standard format. E.g. you used a payroll service and want to bring it back inhouse or move to a different service provider. You need to make sure your master data can be exported and that you have the reports for historical records. When covered in reports, you might get away without transactional data. Typical formats are: CSV, JSON, XML
As you can see, not rocket science, but a lot to consider. For all options the same: do you have what it takes to move? Is there enough bandwidth (physical and mental) to pull it off? So don't get carried away with the wedding preparations and check your prenuptials.