with a mountainbike you have 2 choices of equipment.
1. Bikejoring
2. Underseat attachment.
1. Bikejoring
this is an attachment which attatches to the front of the bike under the handlebars.
It has a guide to stop the lines from snagging on the tyres.
the lines go off and attatch to the dogs via an 'X'Back type harness.
2. Underseat Atachmnet
The two types of these are the "Walkydog" and the "Springer"
Both work in the same way. They attatch under the seat of the bike and have a spring mechanism which absords the "Tug" of the dog
This is attatched to the dog via a line again to an 'X'Back type harnes
As for the bike Disk brakes are a must, Shock absorbers too.