The German Federation was founded on June 20th, 1850 after many Nationalist rebellions and was finalized with the Treaty of Berlin. It united Prussia, Austria, Bavaria, Switzerland and all the small German states into a Federation. Most other revolutions did fail, but The German Federation succeeded in uniting Germans under one flag and one nationality. The Federation is called the 2nd Reich (in reference to the HRE or 1st Reich). The Federation declares war on a weak France and takes Alsace-Lorraine. This worries the Russians, but is fine with Britain as long as Germany didn't stop trading with Britain as they had with France & Russia. Germany is considered the second greatest power (disputedly) after the British. The two do have decent relations and keep trade going between each other.
Tense times (1850-1914)
France & Russia form the Double Entente in 1855. Britain refuses to join the Entente, but also refuses a proposed alliance with Germany. In 1875 Germany, a newly formed Italy and (the beginning to decline) Ottoman Empire create the Triple Alliance. British voters vote to join the Double Entente in 1880 (changed to Triple Entente after Britain joined). This makes Germany anxious but the British promise they will not intervene in conflicts as long as Germany doesn't attack them or Belgium (an ally of the British). The Germans are reluctant to accept the British siding with the T. Entente, but they eventually accepted it and move on to internal affairs.
Wilhelm Era/Germany's Golden Age (1861-1888)
During the tense era, Germany peaked. German industry surpassed British industry (much to everyone's surprise) and an ambitious man took control, his name was Wilhelm. Wilhelm dreamt of a Germany who's power was unmatched and who's colonial reign would rival that of even the British. Wilhelm's relatively short reign did change much in Germany, including industrial progress unseen prior to his reign and a military and navy that even made the British ancy. He pretty well led the German Federation into preparing for WW1. This period pretty much led directly to WW1.
The First World War began as it did in OTL except Archduke Franz Ferdinand was to become Monarch of the Federation as his uncle Franz Joseph was Wilhelm's chief chancellor. This led the now leader of Germany, Wilhelm II (Wilhelm's son) declaring war on the T. Entente (including Belgium and as an extension, the UK). Italy and the Ottomans remain loyal and another nation of Bulgaria decides they want a piece of Serbia and join the Triple Alliance as well. The Triple Alliance would lose WW1, but only because the US entered the war in 1915 as soon as news of the Lusitania was heard. The War lasted until March 7 1919 when an armistice was signed and was soon followed by the Treaty of Versailles.
Interwar period and German violation/disregard for the Treaty of Versailles (1919-1939)
At first, German's accepted the terms of Versailles. It destroyed and ended the Federation and made two German states: Germany (The Weimar Republic) and Austria. However, in the late '20s, spurred by German poverty, the Nationalist Socialist party begins a revolution in 1928. The Revolution soon takes Germany by force and Nazi Germany is made official in 1932. A young man who served in WW1, Adolf Hitler, is made the Führer of Nazi Germany. People cheer him on every occasion and he re-arms Germany, disregarding Versailles and even re-arming the Rheinlands and Alsace-Lorraine (although under de facto French rule). This angers France as they tell Hitler to knock it off, but he merely snuffs at the idea of disarming any of Germany's armies. Germany annexes bordering Czechoslovak areas in the Treaty of Munich and annexes Austria (as he promised to "restore German honor"). The British also become worried as they don't necessarily have their former Dominions/Colonies to help them in case of another World War. The next Great War is set to begin.
World War 2 (1939-1944/5)
World War 2 begins with Hitler's invasion of Poland like OTL. Hitler's puppet of Slovakia does not actively participate, but does arm Nazi troops going through Slovakia. All of the war go as in OTL, with German-Soviet non-aggression pact and their invasions and annexation of Poland and US intervention, etc.
Revival of German Federation (1980's)
The German Federation comes back in the early '80s when German Nationalists rebel much like in 1848, but in 1983. The German Federation becomes a NATO allied nation and consists of it's original territory before WW1 (excluding Alsace-Lorraine).