Basel to Lauterbrunnen train(s) advise

You would book the time you want to travel and it will tell you where you need to change trains
This site might be easier.
https://www.trainline.eu/train-times/basel-sbb-to-lauterbrunnen

It says the fastest journey is 2:23 minutes but it all depends on what time you are try to go.
For sure Basel to Interlaken Interlaken to Lauterbrunnen is most convenient. Choose the one with one change there will be no direct trains and all others have 2 or 3 changes.

Thanks so much for the link and the information on the transfer of trains in Interlaken!

carolego, I am not sure what you do not understand.
At the risk of being facetious: You go to the station, buy a ticket from Basel SBB to Lauterbrunnen (assuming you don't already have a ticket or a pass), either from the manned ticket office (on the left from the main hall), or from one of the ticket machines (faster).
Walk to the platform, and get on the next train heading in the correct direction.
There is one train going the correct direction every 30 minutes. If you buy your ticket from the manned counter, the ticket seller will tell you when the next train goes, and which platform.

You can look up times in advance on the SBB (Swiss Federal Railways) website: https://www.sbb.ch/en
For example, if I enter Basel SBB to Lauterbrunnen, a suitable date and time=11:00, click on "search" it gives me:

Basel SBB dep 11:31, Lauterbrunnen arr 13:55
Basel SBB dep 11:59, Lauterbrunnen arr 14:25
Basel SBB dep 12:31, Lauterbrunnen arr 14:55
Basel SBB dep 12:59, Lauterbrunnen arr 15:25
Basel SBB dep 13:31, Lauterbrunnen arr 15:55

And so on. Swiss train times are boringly clockwork repetitive.
If you click on one of the selections, it will show you where and when to change trains, and the platform numbers.
The train times don't change, they are the same every day and the times have now been fixed up to December 2018.

Agree that Basel-Interlaken-Lauterbrunnen is the most efficient connection. One proviso is stopping in Bern is a delight. The station makes a great base for a 2 hour walk around a beautiful city. Consider routing through Bern if that has any interest to you.

No matter which route you take, you will change trains at Interlaken OST (not West).
You will get the Lauterbrunnen train (typically on track 2A) and make sure it says Lauterbrunnen on the car, because the other half of the train (separates later) will say Grindelwald, which you don't want.

Travelling from Basel to Lauterbrunnen, you always go via Bern (Basel - Olten - Bern - Thun - Spiez - Interlaken - Lauterbrunnen, plus other stops). The question is where you change trains, you always change in Interlaken Ost, sometimes you need to do an extra change at Bern or Spiez.
Having different "routings" does not usually apply to trains. Railway time websites will always find the quickest route. Other routes will take longer, and may cost more. Basel to Lauterbrunnen is one train every 30 minutes.

All very helpful, and just what I was hoping to receive as replies. Thank you so much everyone! The more detail, the better, I always say!

A few minor points to add (you may be aware of these)......

There are two stations in Interlaken, east and west, and the trains to Lauterbrunnen depart from Interlaken Ost (the second stop). Also be sure to check the small digital display on the side of the Berner Oberland-Bahn, as some trains split in Zweilütschinen.