I have never run in my life until recently where I have been making a small effort to get get fit.

I started running a mere 2km a day at 8km/h which I could quite easily manage in terms of cardiovascular fitness but after about a week I had smashed my knee up pretty bad so I stopped for a few weeks and have been doing 4km every Sunday at 8km/h (30 minutes running). I can manage this fine, and will this week start doing 4km on the cross trainer once a week mid week.

Now I know my speed and distance are both small but I'm a beginner so I'm doing ok, but now I need to try and build on what I'm doing. I can either try to increase my speed or increase the duration of my run.

What should I aim for? I am really looking for a target speed / duration that is a good target for somebody new to running to aim for after a few months. Where should I aim to be in a year?

With an existing knee injury, I would suggest that rather than running, you take up swimming - it's great cardiovascular exercise whilst being less strenuous on (knee) joints.
There's a great pool near you, too.

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knee has recovered now, I've done 4k last three weekends with no issue.

It's not about how far you run but for how long

It depends if you are trying to get fit or to impress others (for the latter the shorter it takes the better). I detest running unless you are hunting with a spear or some similar manly activity. Cycling or swimming are far more fun

BigD

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It's worthwhile setting a target which is achievable.
I have a wedding later this summer for which I've set a target, for example, and another target for later this year.
Do a weigh-in and chest/waist/bum-measure and based on that set your target weight/size.
Or set a fitness benchmark now and establish a target based on that, for example, looking at the klms per week you run, or a target heart rate.
As BigD said, it's all dependent on if you're looking for better overall fitness, or weight reduction or other targets.

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Bring on Summer!

Even if your knee isn't hurting now, I would recommend you to start doing something that doesn't demand so much from your joints. The most likely thing is that it will happen again... I don't want to be a party spoiler, but having been fighting with one of those for several decades, I have learnt that the more you can spare them from strain and stress, the longer they'll last.

Anyway, maybe if you start practicing for one of these laufen around Zurich? The Greifenseelaufen will be in September and it seems to be good fun. You can run either 5k, 10k or the half marathon. There is event a family and kid event in the morning.

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I'm afraid somebody will overtly jog up to me and start screaming "i'm jogging man, look how fit I am" in my face should i go to such an event.

Some of them get ultra competitive, but other are more like a a day out for the whole family... Greifenseelauf could be a good one to start, I believe (I am not a runner, but I go to these events in the capacity of Mr Lucy's fan and supporter... )

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... while you are standing at a pedestrian crossing and they are hopping from one foot to another like incontinent loon.

BigD

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www.shootingthecheese.ch
The place for fun and chat in Switzerland.