How did the British planned to attack the Germans at somme

A week long artillery bombardment would destroy the German trench system, kill all the defenders, and allow the attacking British troops to take over the empty German defences from where they could initiate a drive on Berlin that would end the war.

The plan failed. The bombardment was largely ineffective, in many places not even cutting the German barbed wire. German troops sat out the bombardment in the safety of stollen, deep underground concrete and steel bunkers designed and built for this purpose.

As soon as the bombardment ended, the German troops were able to man their largely intact trenches and shoot down the advancing British, exposed in No Man's Land, long before they got anywhere near the German trenches. After 4 and a half months, a strip of land 20 miles long and, at its furthest penetration, 7 miles deep had been captured at the cost of 420,000 British casualties and over 200,000 French casualties.

So, the British plan was a disastrous failure.

The French and British had committed themselves to an offensive on the Somme during Allied discussions at Chantilly, Oise, in December 1915. The Allies agreed upon a strategy of combined offensives against the Central Powers in 1916, by the French, Russian, British and Italian armies, with the Somme offensive as the Franco-British contribution. Initial plans called for the French army to undertake the main part of the Somme offensive, supported on the northern flank by the Fourth Army of the British Expeditionary Force (BEF). When the Imperial German Army began the Battle of Verdun on the Meuse on 21 February 1916, French commanders diverted many of the divisions intended for the Somme and the "supporting" attack by the British became the principal effort.