Classic Skarner Jungle

Standard start

Spirit of the Ancient Golem gives us a tenacity while also giving us an insane amount of survivability while also being very cheap. This enables us to go Ninja Tabi to deal with auto attack champions more easily. It also gives 10% CDR which helps a lot with shield up time and R cooldown.

Ninja Tabi Since we already have tenacity from Spirit of the Ancient Golem . You could consider Boots of Mobility if you are looking for map presence.
Heart of Gold into Aegis of the Legion Aura items give an so much stats to your team and are mandatory. This gives you a good mix of HP from Spirit of the Ancient Golem and a good mix of resistances. In a team fight, the aura is worth about 2500 gold for a 2150g item and we aren't even including the stats it gives. Upgrade to Runic Bulwark as soon as possible if they have a lot of magic damage, if not you can wait to upgrade later.

Sheen If we are massively fed and are snowballing, we may want to consider skipping Heart of Gold and Aegis of the Legion in order to get more damage to build towards a Trinity Force .

Depending on the situation, those are the items you should target after your 2 core items.

If you are looking for more damage items, target the following items:

Trinity Force gives every stat you want. The sheen procs are also very easy to do with the spammable Crystal Slash (Q). The movement speed also makes it very hard to escape you. By far the best snowballing item you can buy.

Wit's End gives you a fair amount of attack speed, which will let us reset the CD of our Crystal Slash (Q) Crystalline Exoskeleton (W). It gives a fair amount of on hit damage and a fair bit of MR while being very cheap. This is a good snowballing item against magic heavy enemy teams.

If you you are looking for more defense, target the following items:
Frozen Heart Great at shutting down auto attack based champions like Tryndamere Vayne Teemo and pushes us to 30% CDR. The extra mana pool goes a long way with how spammable our abilities are.
Runic Bulwark Improves the already powerful aura from Aegis of the Legion and gives us a large amount of MR. Mandatory item to have in teamfights.

Spirit Visage Best MR item in the game and let's us push to 30% CDR. Great against heavy magic compositions. I advice getting Randuin's Omen or Thornmail as our armor item if we build this item to not overcap on CDR from Frozen Heart.

Force of Nature Great sustain and mobility MR option. Let's us have better engage power. Great against heavy AP comps in combination with other MR items or as your MR item if you built Frozen Heart. Works especially well with Shurelya's Reverie to zoom in and Impale (R) a high value target.

Randuin's Omen Good mix of armor, life and utility with the MS/AS slow active. A must against AD heavy compositions and good in combination with Spirit Visage.

Banshee's Veil Anti poke and good when engaging since the shield will often time block an important CC ability.

Thornmail Situationally good vs heavy ad comps, but really uncommon with the current champion pool.
Chalice of Harmony if we can build Frozen Heart due to facing high magic damage teams, I advice building this to fix our mana problems while also getting a nice bit of MR for a cheap price. You can consider upgrading to Mikael's Crucible later.
Guardian Angel Amazing in teamfights and against teams with a lot of burst / low sustained damage. Works well if you are fed and are a main target for the enemy team.

If you are looking for more utility, target the following items:
Locket of the Iron Solari Another aura item that gives your team more stats and the active shield ends up giving a lot of health in gold value for how cheap the item is. Very strong against Karthus Requiem (R) and other AoE abilities.
Shurelya's Reverie enables you to reach 40% CDR when combined with Frozen Heart or Spirit Visage and Spirit of the Ancient Golem. Gives you great engage power which enables you to Impale (R) high value targets in teamfights.

Sightstone Great option to consider after finishing Spirit of the Ancient Golem for more vision control. Better when you need to play a supporting role for your team.

Items to avoid that I've seen a lot of Skarner build:
Madred's Bloodrazor is too expensive for what it does and Trinity Force is a better item for the same cost and Wit's End is a better cheaper option.

Feral Flare is too slow and makes you too squishy in the mid game where you are supposed to be at your strongest.

Spirit of the Elder Lizard while this isn't a bad item, we don't have enough ad ratios to benefit from the AD and has the same problems as Feral Flare in the mid game.

Frozen Mallet or Iceborn Gauntlet you already have a built in slow in your kit from Crystal Slash (Q) so I don't see the point in getting an item that slows when you auto attack. The stats on those items isn't very good for how expensive they are and you get no value from the slows.

Warmog's Armor a lot of our power comes from our very powerful Crystalline Exoskeleton (W) which gives attack speed while the shield is alive. This shield doesn't scale with HP, so getting resistances and CDR is much better for defense and for offense to allow the shield to persist longer and be used more often. This item allows us to do neither.

Boots of Swiftness slow resistance is a bait stat. If you are slowed by 30%, the slow resistance will only reduce it to a 22.5% slow, not to a 5% slow.

Recommended builds:
Fed / Carry:
Spirit of the Ancient Golem Boots of Mobility Trinity Force Guardian Angel Frozen Heart Wit's End

Standard:

Spirit of the Ancient Golem Ninja Tabi Runic Bulwark Frozen Heart Shurelya's Reverie Force of Nature

Against AD heavy teams:
Spirit of the Ancient Golem Ninja Tabi Runic Bulwark Frozen Heart Randuin's Omen Shurelya's Reverie

Against AP heavy teams:
Spirit of the Ancient Golem Ninja Tabi Runic Bulwark Spirit Visage Shurelya's Reverie Banshee's Veil

Utility tank:
Spirit of the Ancient Golem Ninja Tabi Sightstone Runic Bulwark Frozen Heart Locket of the Iron Solari