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I've been playing Arachne for a long time now, and I see that shes a pretty strong god even though most people say shes useless and under powered. She can either be built as a semi-carry or full on carry. This guide is built as a semi-carry.
Get Broodlings as your first skill and run to the blue minion camp and place 2 eggs right outside the camp. Then run over to the speed camp and place two more eggs there. When the minions spawn, use your Hand of the Gods and kill the speed minion. Then run back to the blue camp, and if the other team hasn't destroyed your eggs yet, place one more egg and clear the blue camp. If they have you can still clear it, it will just take a little longer. Then go to the yellow camp and finally green.
At the end of this, you should still be level 3, almost level 4. You should gank your left lane now. After killing both people, you should be level 5 or almost level 5 and from then on, you will have a huge advantage over everyone else. Even though I say this is the order, you can gank any time the opportunity arises.
When ganking early, place your eggs far behind the other people so they dash or leap into your eggs (but not so close it gets destroyed). This not only provides damage, but more importantly a slow.
After ganking left lane once, your laning partner (if he hasn't died) should be well off too. You should go and gank other lanes that are overpushed. If every lane is doing fine, then just stay in your lane.
Your team should be pushing towers now and you need to use your Cocoon cocoon to web someone back into your team. Usually, that person instantly dies. You can also easily pick off people who stray away from their team.
Arachne needs to initiate team fights with her Cocoon. It's the perfect way to get the strongest person on the opposing team to die. If she misses, with this build, she can just charge in and tank for a few seconds. Arachne often seems to be the first to be focused for some reason, but usually your team will be able to kill the enemy gods shortly after they've taken you down.
When in the ganking phase, you should approach them from behind, hit them a few times and use your Cocoon to pull them back to you when they dash or leap away.
Remember to time your silence from Drain Life. If someone just leaped away and you Cocoon them, usually it's not a good idea to silence them straight away. Instead just carry on hitting them, and after a few hits silence them as their cooldown on leap is about to finish.
Since you are jungling, you need a laning partner that can solo. Preferably someone with a slow or stun. My friend always goes tank Vamana and solos. Generally, I don't like it when mages solo left lane as they just die too easily. Therefore my choices are Vamana, Cupid, Anhur and Guan Yu.
Yes, even with the Mystical Mark glitch that just happened, it's a great early item for Arachne. It gives you HP, and adds damage to your drain life. Later on, you can replace it with anything else you see fit. Remember that you need to get Hand of the Gods at the beginning of the game! I only started used this build after the last patch when they changed Ankh of the Golem to attack speed. It allows Arachne to deal damage while being tanky at the same time.
You need to be careful if you follow this build because you will die fast. Starting items are still the same (Hand of the Gods first). Before the last patch, I used Soul Eater instead of the Ankh of the Golem.