Before i start explaining let me just say that this is my first costum build, but i do know the pros and cons of sivir and how i usually play with her, and if any of you disagree then please say so BEFORE rating this build, so i can discuss your opinion of this build and how it might be better.

the tips on farming i would have, is to start of the game in mid lane and keep farming minions until sivir has her ultimate, and then switch with another champ mid to keep all lanes occupied. When you have switched you can roam about freely to do major farming and pushing where needed, this is usually a very successful tactic and the money and power just keeps coming. One minus point to this tactic is that sometime you can become predictable and therefor lose the sense of surprise.

based on how i play sivir, i am usually an aggressive attacker and i don't concentrate on my health being sufficient during an ongoing attack, because of this i depend (maybe a bit 2 much)on health items as to keep me alive.
During an inspection of all these health items i realized that the items i chose in this build help me with my health issue whilst still giving a powerful punch in passive and active abilities.
When not in need to "upgrade" the health then i would say, instead of using: Heart of Gold, Ionic Spark and Warmog's Armor; go for the Hexteck tripple combo ( Hexteck revolver, Hexteck gunblade and Hexteck sweeper) for they add a deadly punch on ability power and for the gunblade also a bonus attack damage

as mentioned above i usually go for the health items, and after having a good look at all of them i thought the above items where the ones that packed the most punch whilst packing the most punch.

For example: Entropy and Frozen Mallet both add a bunch of health and also have a slowing effect, adding this to sivir's passive Fleet of Foot can ensure you that the opponent has less chance of getting away from an attack.

another example is Ionic Spark, as it is a good addition to attacks, for example when farming close to the enemy base as to clear the way for allied minions

as you can see the build i use is to make sure that with my temptation to go right into battle and have a high risk of suicide i chose a HUGE health build, whilst still keeping in mind that i need to be able to do some damage, and this is the result of my "investigation" and if u use this build with sivir or any other character then plz tell me the result and the possible improvements to the build u would think necessary