Well you have two times when you think about item building. Pre planning a build and in game adaptions of what items to buy. You should also understand the full picture of your build, not just items but runes and masteries and as well.
Planning a build, you obviously want to pick items that augment your champion's kit. Round out their weaknesses efficiently and then play to their strengths. You generally presuppose a balanced enemy team. Understand that build order matters, that build flexibility can be important too. You need to know your champion and their role in the team.
To make an example, I'll look at 
.
Now things I know about the champion are
- Vel'koz is an APC
- Vel'koz needs a little mana help
- Vel'koz has poor AP ratios
- Vel'koz has a high base movespeed
- Vel'koz has long range and AoE
- Vel'koz's ultimate has a long cooldown
- Vel'koz is fragile and few escape skills
- Vel'koz has two slows and a knock up
So. I'll need to get mana somewhere, naturally. But more importantly, I want to build damage on him because that's what he does. Its what gives him presence. However he has poor AP ratios. So I will look for damage in other fashions from other items. Theres procs, CDR, mpen, and Liandries. And if I can get AP along the way, it won't hurt. I also want to survive with him, but he lacks both escapes or defenses. So, I realize I have to use his base movespeed and range and slows to control positioning. I also know mages can build Zhonya's as a defensive substitute against diving enemies.
Now we can consider the various mage items.
- Has mpen, looks kinda nice. But its aura may be too short for Vel's range.
- that will solve my mana
- that will not only solve my mana, but it also increases my mr a little and gives CDR, increasing my dps and reducing my ult's cooldown. Good item.
- this has a proc based damage source and goes well with his base movespeed. Lots of AP too. Good item.
- that will solve my mana and give me CDR. Its passive could be useful against certain enemies. It doesn't give me MR, but its cheaper than Athene's. Good item.
- a ton of AP. It doesn't fit my plans, but its ssooo powerful it just might work anyway.
- Some HP and AP, doesn't synergize with my AoE. Not what I'm looking for.
- %mpen, that should definately help my damage late game. Good item.
- Mpen, HP, and an outside damage source which works best with slows and when given time to do its work. Definately Vel's type of item.
- This could solve a lot of defensive concerns, and it at least gives me high AP.
We can narrow down some of the items and draw up a build from the remainder. are all worth consideration. But we can only pick 5 right now, and order matters.
In the end, I pick . I also select 
for boots. I think that this gives me a number of offensive scaling abilities, and a balanced defensive profile. It solves my mana problems and has a little MS thrown in as well. But I'll keep the other rejected items in mind for now.
So now we get to our build order planning. Without knowing exactly what I'm facing, it can be hard to decide. I have to be ready to adapt this build to what I'm facing. In general however, I want to solve my mana concerns and build the damage that's my job to do. As a damage dealing champion, Vel has the luxury of only building defense when he feels its necessary. So, my build order runs around a core path that completes what Vel needs for presence - damage and mana, and optional defensive choices.
He needs 
to solve his mana. is the biggest damage item in my build early game. Getting it and also helps his mobility to roam and avoid ganks as a mid laner. Finally 
affords him a strong early game mpen boost and hp, while building into an item we'll use later. So my standard core build becomes 
. This gives Vel'koz a lot of firepower and solves his mana. It also gives him some defenses and several further build options, in finishing his unfinished items. But it leaves him vulnerable to something: the AD assassin! But his final build does have an answer to this, So Vel needs to be ready to buy to deal with Zed or other similiar champions. Finally, he may to wish to counter his enemies own champions. For example, 
. He has strong sustain that may shrug off Vel'koz's damage. But in our previous pool of items, we had an item that fit Vel'koz and answers Swain. . When facing off against a Swain, it might be wise to build this instead of its closest equivalent, Athene's.
Anyways, this got longer than I expected. But I had fun writing it.
If the whole team has alot of AD build like Omen's or like Sunfire cape.
And WalkingInACircle said that champions like vel'koz need items that could help him alot in late like a Zhonya's