If you are submitting your app for security review ,you will need to enforce CRUD-FLS for all your DML and SOQL since apex does not enforce it automatically.
There is a blog post link below that shows how to enforce CRUD FLS
https://developer.salesforce.com/page/Enforcing_CRUD_and_FLS
You will use describe call to find the access level and prevent the DML if user does not have sufficient access .
If your project has lots of apex then you may want to use some library that's build to specifically handle heavy lifting of checking CRUD/FLS .The project is open source here
https://github.com/forcedotcom/force-dot-com-esapi
The project has utility methods to wrap the DML to perform checking of access before any DML .
Note that if you are not building a managed package and instead customizing single org and if there is no strict requirements around security enforcement you may skip these checlmarks warnings