Rendering internal brick walls

Hi mate.
Are you talking the whole house?

Any form of hard plastering isn't going to be a DIY type of job if you have never done it before.

Hard plaster is very messy because it's a wet trade. The walls have to be wet down as you do the work.
There are 2 coats that get applied. A "float" layer that is a mix of sand, cement and lime that is trowelled on at about 10mm. This is used to flatten and straighten the wall. All external corners have plaster beads applied before this float layer is applied. This layer leaves a sandy slightly textured finish.
After the float coat then a "set" coat is applied. This is just a thin coat of plaster or gypsum that gives the smooth hard coat that can then be painted.

The work is messy and wet therefore any floor coverings would need to be fully covered, but even then it would be a struggle to do this without it being part of a full reno.

Usually the easier method is dry lining. That's where plasterboard sheets are stuck directly to the brick work and then flushed.
It's a lot cleaner to do this as you don't need to wet down the walls during application. It's still not really a DIY project if you haven't done it before or aren't familiar with the process.

Both methods add about 10mm to the existing walls so there are a number of issues that you need to consider.
The cornice, architraves and skirtings plus any power points and light switches will all need to be considered as the walls will all be built out 10mm.

The simplest and most DIY way of changing the look would be to just paint the brick. It would be time consuming as painting raked motor joints is fiddly but it's definitely the easiest and most DIY friendly option.

Good luck