When you get a half season ticket it's essentially the same as having one of the old memberships- u get first pick of the tickets before general sale, so you just then buy the tickets either online, over the phone or from the ticket office, stating your season ticket number if you have to.
In terms of sitting next to that person, the only way you can really do it is by making sure you get a season ticket that does not have another season ticket holder next to it (the ticket office can tell you that) and then make sure you get the ticket as soon as it goes on sale so noone gets it first.
HTH