The south face route is the most popular with huts above the snowline extending from 3800m to 4100m. Most people make use of a 'ratrack' or piste groomer to transfer up to Pastukhov Rocks at 4650m which still leaves a long summit day ascent of 1000m which takes around 7 - 10 hours.
The north side is not as facilitated, it's a wilder more remote experience. It's not technically difficult, about a PD alpine grade, but it's a 1900m ascent on summit day which is commonly between 12-16 hours. There are a few huts on the moraine at 3750m, and a small higher campsite at Lenz Rocks which is 400m higher.
To get to the higher west peak, climbers have to traverse through the long col between the two peaks and join the south route, or potentially ascend directly to the summit plateau.
Make sure you read our page on preparing for Elbrus so you are well informed before going on this trip