First thing to remember is that builds are not set in stone. What works one game may not be the best for the next. Sometimes you will build the same items but in a different order, sometimes you will build different items based on the enemy team or situation of the game. Generally, champions have a "core build". These are the items that will be built the large majority of games and will generally be built as the first few items. Outside of your core build, most items will be situational.
TL;DR - Item builds depend on what you need to be able to do for a given game. There are several websites that have build suggestions and/or guides (mobafire.com, probuilds.net, lolking.net, and many more).
Taking Blitz support for example (I haven't played Blitz hardly at all, but have seen him in many games I've played), coin (for gold, some lane sustain, and when fully upgraded, an activated team speed boost), sightstone (for vision. make sure you use it after you buy it, it doesn't magically place good wards for you), and mobi boots (for getting into position for a grab) are probably his core build. To go from there, we need to consider what the team is expecting from a Blitz support. The support is generally not expected to be a major source of damage. They are, however, generally expected to provide assistance to the team in the way of cc and protection for the damage dealers. Blitz already has some very potent CC in the form of his hook (which is best used to pull someone out of position for your team to kill, rather than for solo plays) and his area silence (also best when used against multiple targets to protect and set up the primary damage dealers). The best way to provide more CC is to get cooldown reduction (CDR, remember any over the 40% cap is wasted) to get your skills up more often. The coin upgrade provides some, and several defensive aura items do as well (allowing you to double up the usefulness of an item).
Two very common items for supports are 
Frozen Heart (armor, mana, CDR, enemy attack speed reduction aura) and 
Locket of the Iron Solari (allied magic resist aura, activatable team shield). As you can imagine, these two items are built to defend against two types of damage sources.
Frozen Heart is good for cutting the damage of ADC and other auto-attack reliant champions (Tryndamere, Yi, Xin Zhao, etc). As a point of consideration, you might notice that Thornmail is also good against auto-attackers, but in general, the support is not the focus of these champions, and Thornmail does not give as many other stats that you want, so Frozen Heart is generally the better buy for supports since it defends you if you do get attacked, but is still useful if you do not.
Locket of the Iron Solari is good for cutting all magic damage done to your team, provided you are near them. In addition, it has a nice activatable shield that can protect against AOE damage if timed well (any type, not just magic). There are other items that build out of the 
Aegis of the Legion component of the Locket that gives the magic resist aura, and some of them may be more useful depending on the circumstances.
If you are facing an all physical damage team, an Aegis of the Legion (and its upgrades) is not a good buy. Similarly, if the other team is primarily magic damage, or have no auto-attack champions, the Frozen Heart is not as good of a buy. In the end, you have to pay attention to how the game is flowing and build accordingly.
About 
Black Cleaver specifically, it is not a good buy for Blitz support. While it does have 20% CDR and some health, there are other items that provide just as much with other stats that Blitz wants more. The AD is largely wasted because Blitz (especially as support) is not focused on doing auto-attacks for damage, and only one of his abilities even scales with AD. Additionally, neither of the passives on Black Cleaver are especially good on Blitz. The Rage passive is not needed for Blitz because he already has a skill speed up and will generally build Talisman of Ascension. The armor shred effect is not very good for him because he does not have a good way to stack it quickly (as opposed to say, Garen or Riven, who can quickly apply multiple packets of physical damage to fully trigger the effect).
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I've mostly figured out my builds for these three but I still have doubts every game. For example, when I Blitz support, I always find myself debating whether Black Cleaver would be good for me. It seems completely counter to other support builds are like. I find Blitz damage late game is really something that needs to be built.
these are some verry good items for suportng
if someone says not there lieing just ignore them
