Based on a Lavos skeleton and fleshed out by me
Blissey is one of the tier's only clerics while also functioning as a solid Special tank. With humongous HP and Special stats, there's little she fears under normal conditions (beware of maxed out Vaporeons, cause they might crit you eventually or stall Softboiled's PP out). She can even take a few physical moves in case you mispredict and heal up fairly safely. Her offensive presence is terrible though, so, aside from tanking hits and supporting its teamates defensively, the most you can expect a Blissey to do that annoys the opposing team is spreading status and hitting them for pitiful damage.
Move 1: Softboiled
Move 2: Heal Bell
Move 3: Flamethrower / Light Screen
Move 4: Toxic / Light Screen
Softboiled and Heal Bell is the support combo you really can't afford to change. Heall Bell works especially well with RestDrum strats, waking up its sleeping teamates after they (hopefully) spread havoc with Belly Drum and healed up with Rest, but it can function on any team that wants to be kept out of status. Softboiled is what keeps Blissey alive without having to spend two turns sleeping, like most other Pokemons on the tier do. The rest of the moves can be tailored for whatever supporting need you might want Blissey to have. Flamethrower serves as a general attacking move in case you don't want her to be the most passive thing in existence and hits Steel types that might switch in expecting you to use Toxic or just wanting free turns on you in general. Savor those moments because they are basically the only time Blissey actually hits something hard (even though it's still only a 3HKO on things not named Scizor or Forretress). Light Screen might seem redundant at first, but it's there so she can be even more of a defensive support to your team, providing a few safer turns for any teamate that wasn't blessed with her Special Defensive prowess. Toxic is the main Status move, which, together with Flamethrower, ensures she can at least do something offensevely to every Pokemon. The chip damage Toxic provides applies general pressure, especially together with Spikes and might be crucial to force an opponent to Rest earlier.
Sadly, Blissey has move compatibility problems so some powerful moves like Counter and Reflect can't be used together with Heal Bell and it's really just best to keep Heal Bell. The most common other moves are Sing to fill the role of a sleep user and Ice Beam to offensively threaten Zapdos and Ground types, but Flamethrower is usually prefered, since it handles both Spikers in the tier much better, who will switch freely into Blissey that don't have it. Growl can also be used as a very niche option to PP stall the opponent and lower the offensive presence of physical attackers that might switch into Blissey, maybe even neuter a Curse user, but Blissey's moveslots usually have other much better uses, as this makes her even more passive and there are already enough natural physical tanks in the tier due to Snorlax's omnipresence
[CHECKS & COUNTERS]
Blissey excels in supporting her teamates and there's little you can do to stop that aside from waiting for her to burn Heal Bell PP, but there are a lot of ways you can force her out or mitigate her effectiveness. She always has to fear Explosion and is slower than many of its users which further complicates things. Snorlax has free switches into Blissey on almost all cases and has little to fear if it's packing Rest, since Blissey can't really threaten it with either Flamethrower or Toxic, while being able to hit her hard on the physical side right off the bat, so having a direct pivot to answer all forms of Snorlax is important when using Blissey. Marowak and Machamp also deal a ton of damage to her and are good ways to instantly force her out, but some of them might fear being Status'd. Blissey can actually tank a lot of physical moves due to her insane HP, but healing up from it might be costly enough PPwise that you can force her out by spamming physical moves. Since Blissey has little offensive presence, basically anything that doesn't fear Status and her coverage move can switch in safely and proceed to set up or just cicle switch endlessly while taking negligible damage until she runs out of PP.