I recently bought an urban bike that comes with a single gear crankset with a 42 tooth sprocket and an 8 speed rear with 12-36 teeth. I would like to swap out the front sprocket to a larger one to gain more top end speed. I'm thinking 48-53 teeth depending on what I find. I wonder how I would go about doing this. Can I just screw off the 42 and attach a 48 to the existing crankset and then lengthen the chain a bit? Or would I need to purchase a new crankset? Would I need to adjust the rear derailleur if I run a larger front sprocket?
Rather than trying to lengthen the chain, I would recommend you buy a new one as you will be much less likely to have a tight or bent link this way.
You should not need to make any adjustments to the derailleur if you are only changing out the front chainring.
This is a fairly standard looking crank, chainrings should be readily available in a variety of sizes.
When I searched on the specs the pictures and listings didn't match, so you'll have to measure to be sure what you have in front of you.
However, you might want to actually try riding the bike as it is, turning your legs at a fairly standard 90 rpm is around 40kmh with the top existing gearing.
The general answer is, "yes, you can change chainrings" – chainring is bicycle talk for the front sprocket. The more specific answer will depend on the actual crankset the bike is built with. There are some that don't make it easy to remove a chainring or where replacement rings are hard to find. To know for sure you'd want to have the bike in hand and check – unless you know the make and model of the crankset that comes with it.
All of that said, I think it would be a good thing to hold off for a while on changing anything. In general (again) pedaling at a higher speed (meaning higher RPMs which cyclists call cadence) is easier on your knees and overall endurance. So I'd encourage you to experiment with the existing setup first. At 70 RPM, which many would consider to be on the low side, your top gear (42x12) will give you about 32 km/h (20 mph) and up at 90 RPM you'd be doing 40 km/h (25 mph). Those are respectable speeds on the flat. Downhill you'll be able to go faster (if you want to), but at some point you'll "spin out" and find that you can't pedal fast enough to push the bike any faster.
If you do decide that you want more speed (or more speed at a lower cadence) then you have two options:
A larger chainring in the front (which will make all of your gears higher), or
One or more smaller cogs in the rear (which will make the individual gears higher). The easy way to make this change is to buy a new cassette (the set of rear gears). You could go to a cassette with 11 teeth on the small cog which would take you up to 35 km/h at 70 RPM.
The advantage of changing cassettes is that the interface is pretty well defined (unlike chainrings where there are lots of little gotchas) and the cost is lower (in general). Over time you'll wear out cassettes, so you'll be changing your's from time to time anyway.
If you want to play with possible gearing scenarios the HTML5 Gear Calculator makes it quite easy to see what the impact will be.