Process maps even at a high level are a good start to decide where you can add value in the quickest way. But make sure you question the business process and whether it's effective before just implementing technology around it.
In terms of project management, something like the Scaled Agile Framework (SAFE) will work in an enterprise environment if you're from an agile background. Minimum Viable Products work well in enterprises but it's often a huge mindshift for enterprise customers who think they need every feature.
Charging by day rate is your best option. Enterprise IT projects will generally overrun and scopes will increase. If you're charging by day, you're protected from scope creep.
Make sure you've documented what you're doing clearly and you've got a strong contract. If I need to challenge an IT supplier over what's been implemented, and I often do, the contract is the first place I started. A good contract and clear expectations is a positive thing for both parties.