A common mistake when making the transition to microservices is to ignore the monolith and just build new features as services. This usually happens when a team feels that the monolith has gotten so out of control, and the code so unwieldy, that it would be better to declare bankruptcy and leave it to rot. This can be especially tempting because the idea of building green field code with no legacy baggage sounds a lot nicer than refactoring brittle, legacy code.
Resist the temptation to abandon your monolith. To successfully decompose your monolith by business capability and start evolving it into a set of nicely factored, single-responsibility microservices, you'll need to make sure that your monolith code base is in good shape and is well factored, and well tested. Otherwise, you'll end up with a proliferation of new services that don't model your domain cleanly (because they overlap with functionality in the monolith), and you'll continue to have trouble working with any code that exists in your monolith. Your users won't be happy and your teams' energy will most likely start to decline as the weight of technical debt becomes unbearable.
Instead, take constant, proactive steps to refactor your monolith using good, solid design principles. Excellent books have been written on the subject of refactoring (I recommend Refactoring by Martin Fowler and Working Effectively with Legacy Code by Michael Feathers), but the most important thing to know is that refactoring is never an all-or-nothing effort. Few product teams or companies will have the patience or luxury to wait while an engineering team stops the world and spends time making their code easier to change, and an engineering team that tries this will rarely be successful. Refactoring has to be a constant, steady process.
However your team schedules its work, make sure you're reserving an appropriate time for refactoring. A guiding principle is, whenever you go to make a change, first make the change easy to make, then make the change. Your goal is to make your monolith code easier to work with, easier to understand, and less brittle. You should also be able to develop a robust test suite that will come in handy.
Once your monolith is in better shape, you can start to continuously shrink the monolith as you factor out services. Another aspect of most monolith code bases is serving dynamically generated views and static assets served through browsers. If your monolith is responsible for this, consider moving your web application component into a separately served JavaScript application. This will allow you to shrink your monolith from multiple directions.