Before design is underway you'll want to make sure you have a clearly defined and expressed objective. Designing without an objective isn't really design.
How you measure the success of your design is going to depend on the objective. Both qualitative (quality data such as survey responses) and quantitative (numbered data such as clicks or downloads) methods of measurement can be considered when evaluating the success of a design.
1. Define objectives up-front, before designing anything
An objective can be to get downloads of a product, ensure users can access critical features, increase sales of a product, or even something more tangible, like winning an award.
2. Define and refine the objective with XFN partners
If you're on a collaborative team, refine the design objectives with your XFN (or cross-functional) teammates; product or project managers, design peers, engineers, or clients/customers.
3. Check designs against the objective as you go
As you design you'll want to check your efforts against the objective as you go. Doing so will not only ensure you stay on a productive path, but it will also enable you to make trade-offs faster (e.g. if an idea or pattern isn't going to help with your objective you can safely ignore it).
4. Evaluate factors that contribute to your objective
In addition to simply completing a design, analytics and customer surveys can help clarify if you've achieved your objective. Quantitative or qualitative data in the form of downloads, purchases, click-throughs, or customer survey responses are all good examples of metrics to look out for (depending on the objective of your work). You can also do a retrospective with your team or client to see if the objective was met and other ways you might measure the success of the designs.