Travel from Interlaken to Lauterbrunnen?

I think you want to go to Interlaken Ost (east) which is from where the trains to Lauterbrunnen leave.

The German Rail schedule website shows regional trains every half hour from Interlaken Ost to Lauterbrunnen.

Also, you are not taking EuroRail to Interlaken. The trains are run by Swiss Rail, SBB. Eurail (it's real name) is a consortium of national rail companies, ship lines, et al in Europe organized to package and market rail passes.

Instead of getting of the train at Interlaken West, get off at the next (and final stop) Interlaken Ost. From that station there are trains every 30 minutes or so to Lauterbrunnen.

from Paris ..... I take a EuroRail to Interlaken West

Oh no you won't! There is no such thing as a Eurorail train Eurail is a travel agency selling rail passes and tickets mostly in North America. They do not own or run any trains. Trains are run by an assortment of national and local rail companies. SNCF in France, SBB in Switzerland etc.

Coming from Paris, you may need to change trains in Basel fro Interlaken, or depending on time of day you may get a through train to Interlaken Ost (not West). There you change to a different train (different local company) to Lauterbrunnen. The trains wait for each other.

See this map of the area. Red is rail lines: http://www.berneroberlandtaxi.ch/images/map_2015.jpg

Thank you! You've all been incredibly helpful! One more newbie train question: I'm going to be taking a train from Paris to Interlaken East. Some of the transfer times are only 5-10 minutes. Is that normal? Is that doable for a newbie (first time to a European train station), or will that be total chaos? Thank you!

I was just in Interlaken Ost standing on the platform about 2 weeks ago and there's a big sign that says "Eurail Not Valid". That is to say that you'll need to buy additional tickets because your Eurail pass only gets you part of the way.

Hope you have a great time because the Lauterbrunnen Valley and surrounding alpine villages are stunning.

TIM: thank you! Where would you recommend I get my tickets? Thanks!

Short connection times are easily done on Swiss trains, which run like ... well, like a Swiss watch. Well-organized, timely.

as a newbie, it helps to know that you should pay attention enough to know when you are getting close to the station at which you must change trains. You should be ready, with your bags, to get off quickly and not wait until the doors open to be moving or you could get blocked by slower moving folks, and those hustling to get on as soon as the doors open. If you've ever ridden an urban subway system in the US (BART, MARTA, WDC Metro, NYC Subway, etc. ), its like that.

Many thanks to you all for your excellent help!

RE tickets from Interlaken Ost to Lauterbrunnen. You can buy these at Interlaken Ost station (or any other Swiss station). This costs CHF 7.60, no reduction for advance purchase (see https://www.sbb.ch/en/ ).
Buying a ticket at Interlaken Ost may mean you miss the next train to Lauterbrunnen, but there is one every 30 minutes, so you can look around the town for a while.
5-10 minutes connection time is normal in small Swiss stations. The trains are designed to connect, they stop next to each other, or on parallel platforms, and wait for everyone to get on board.

One more minor point to add.....

When you board the Berner Oberland-Bahn at Interlaken Ost for the short (~20 minute) ride to Lauterbrunnen, be sure to check the small display on the side of the car to ensure that the car you're riding in goes to Lauterbrunnen. Some trains split at Zweilütschinen, and the latter part goes to Grindelwald.

Thank you all SO MUCH for your amazing help!