You buy them. AFAIK there are no schemes or grants available, although I'm sure other people will correct me if that's wrong.
Some energy companies will fit them or you can find a company to do it. Either way, you pay for the charger and you own it. They cost upwards of £1000 installed.
In theory you can disconnect it and take it with you when you move. Most people don't because it's a hassle to remove and a lot of the cost is the installation. You'd pay to have it removed then reinstalled when it wouldn't be much more to get a new one at your new house.
Home EV chargers use something called a Type 2 plug. This is a universal standard for AC charging so all electric vehicles can be charged with a Type 2 charger.
The charger doesn't care which electricity supplier you use. The only time it matters is if you want to use an EV specific tariff that requires the charger to communicate with the energy company. They do this to trigger charging at specific times of day. Each energy company has a list of compatible chargers, and sometimes compatible cars as they can be part of the communication mechanism.
Just to add to the good advice from @M.isterW
There are grants in very limited circumstances, for example if you live in a flat or rent. Further info.
https://www.gov.uk/government/collections/government-grants-for-low-emission-vehicles#ev-chargepoint-grant
You may find in the future you would have to swap your charger if you want to make use of any V2G or V2H functionality, but there isn't much you can do about that as there are only trials going on at the moment.
Had a similar question to OP.
If I buy the charger on OVO energy website, will OVO claim the grant for me from the government? I am currently renting so believe one of the grant is available to me.
I asked Indra chargers and they said they do not claim the grant. Anybody know if OVO helps with this?
I think you may need to claim the grant yourself