The usual aim for PhD applicants would be to get a fully funded PhD, which would include the fees and also a stipend. This is normally through one of the research councils (which one depends on the area your PhD is in). Self-funded PhDs can carry some stigma in some areas (particularly STEM fields I gather), especially if you are aiming to continue in academia (as it's really the first test of your ability to secure research funding, which will be a continual part of working in academia).
The "how" would usually be to apply to the PhD with a very strong profile and, if not a "potted", existing PhD project, to have a very strong research proposal. Note that funding is very competitive (more so than actually being admitted to the PhD), especially in some smaller fields or less well funded fields (e.g. many "arts" fields). A 1st in your undergraduate and research experience would likely be very desirable, a relevant masters in hand may be desirable for some fields, publications would be excellent to have but not normally expected.