Short answer: enough to get your startup to an accretive milestone plus some fudge factor.
“Accretive milestone” is a fancy way of saying getting your company to a point at which you can raise money at a higher valuation. As a rule of thumb, I would say a successful Series A is one where good VCs invest at a pre-money that is at least twice the post-money of the seed round. So if for your seed round you raised $1M at $2M pre ($3M post-money valuation), for the Series A you should be shooting for a minimum of $6M pre (but hopefully you’ll get significantly higher).
The worst thing a seed-stage company can do is raise too little money and only reach part way to a milestone. Pitching new investors in that case is very hard; often the only way keep the company alive is to get the existing investors to reinvest at the last round valuation (“reopen the last round”). The second worst thing you can do is raise too much money in the seed round (most likely because big funds pressure you to do so), hence taking too much dilution too soon.
How do you determine what an accretive milestone is? The answer is partly determined by market conditions and partly by the nature of your startup. Knowing market conditions means knowing which VCs are currently aggressively investing, at what valuations, in what sectors, and how various milestones are being perceived. This is where having active and connected advisors and seed investors can be extremely helpful.
Aside from market conditions, you should try to answer the question: what is the biggest risk your startup is facing in the upcoming year and how can you eliminate that risk? You should come up with your own answer but you should also talk to lots of smart people to get their take (yet another reason not to keep your idea secret).
For consumer internet companies, eliminating the biggest risk almost always means getting “traction” – user growth, engagement, etc. Traction is also what you want if you are targeting SMBs (small/medium businesses). For online advertising companies you probably want revenues. If you are selling to enterprises you probably want to have a handful of credible beta customers.
The biggest mistake founders make is thinking that building a product by itself will be perceived as an accretive milestone. Building a product is only accretive in cases where there is significant technical risk – e.g. you are building a new search engine or semiconductor.
Now to the “fudge factor.” Basically what I’d recommend here depends on what milestones you are going for and how experienced you are at developing and executing operating plans. If you are going for marketing traction, that almost always takes (a lot) longer than people expect. You should think about a fudge factor of 50% (increasing the round size by 50%). You should also have alternative operating plans where you can “cut the burn” to get more calendar time on your existing raise (“extend the runway”). If you are just going for product milestones and are super experienced at building products you might try a lower fudge factor.
The most perverse thing that I see is big VC funds pushing companies to raise far more money than they need to (even at higher valuations), simply so they can “put more money to work“. This is one of many reasons why angels or pure seed funds are preferable seed round investors (bias alert: I am one of them!).