When you lease an IPv4 block, what do you actually get? How do you get access to the IP addresses? Is there any special equipment required or is it as simple as renting a server?
When leasing an IPv4 block, you can either ask your ISP or rent a block from the Network Coordination Centre (RIPE for instance) and this is IF you become a RIPE member. You typically get what you ask for. For instance, if you want a /24 or /28 it wont be any problem to get.
The most common way to lease IPv4 blocks is through your ISP, as they typically have loads of different IP blocks to rent out from, whereas the smallest possible block from RIPE is a /22. Also the chance of actually getting a block from RIPE would be pretty slim, as they tend to reserve blocks for Governments, ISPs etc. as the IPv4 scope is running out.
You can also buy an IPv4 block on an auction. When doing this, you will own it forever and you will pay RIPE, for instance, to announce it via (example) your ISP AS number.
When renting from an ISP, the ISP will register your block as being owned by you on (for instance) RIPE.
When buying or getting a block from an auction or RIPE, you register your IP block yourself by creating an user on RIPE and then you decide however you want to announce it. If you want to announce it via your current ISP, you will need to add routing information on the RIPE LIR Portal. Here you can also edit/subnetting/add descriptions to your IP block.
The last question can be achieved in many different ways. In my organization, we add a route to the ISP official AS number. Then we peer with our ISP via BGP and everything is being announced to our internet access layer/routers.
When you lease an ipv4 block what do you actually get?
The right to use those addresses on the Internet.
How do you get access to the ip adresses? Is any special equipment required or is it as simple as renting a server?
You have two options, if you have BGP sessions established you can advertise the addresses yourself. Alternatively you can get your provider to advertise them for you. Either way you are likely to need to speak to your provider and present them with the evidence that you do in-fact have the right to advertise the addresses in question.
If you don't already have BGP set up and you don't plan to use the addresses for anycast it's probably easier to get your provider announce them.