Again I am new to Netrunner so forgive me for asking so many questions. Question: during the game I install an asset in a remote server, the runner runs on that server and discovers the asset, that has a trash cost, can the runner pay the trash cost before the effect fires, or does the effect fire before it is trashed. If the former is the answer what’s the use in putting assets in remote servers if all the runner has to do is trash it. Take Cerebral Overwriter for example, it can be advanced and i can pay 3 credits to do 1 brain damage for each advancement on it, I pay 5 credits worth of advancement, the runner runs on it but all he has to do is say trash it and I have wasted 5 credits, why would I ever play this card?

You are correct, assets that have an effect that triggers “when the runner accesses” take effect at that exact moment. The choice to pay the trash cost is afterward.

You should also look up the official FAQ and consult the timing chart; it will answer many questions.