If you look for beautiful and scenic places in Japan, this will probably be on your list already. If not, this article might contain a pretty interesting destination to visit on a weekend or just on your trip to Japan.
If you come to this place I definitely suggest you to take one of the sightseeing boats. There are two companies for sightseeing boats, but I recommend the 'Hakone Sightseeing Cruise' one as they have an english version of their website.
A cruise from one end to the other end of the lake costs 1000 yen and takes approximately 30 minutes.
In my opinion, this sounds like a really good deal getting to see such a beautiful view for a moderate price!
Also, the sightseeing boats look like pirate ships which adds a cool feeling to the sightseeing cruise - I mean, who doesn't want to feel like a pirate cruising on a large lake while having an amazing sight?
On the shores of lake Ashi in the town of Hakone sits the Hakone Shrine, which you can't directly see from the lake, but if you're at the lake, you can definitely visit this shrine as well.
Additionally, you can have a look on the torii gate from the lake, which is why I mentioned the shrine.
Further information to the sightseeing of the lake: http://www.hakone-kankosen.co.jp/ (available in English!)
Lastly, a fun fact: Did you know that Ashi-no-ko means Lake of reeds? Interesting title for such a scenic and popular lake!