In short, it was a long fighting retreat relying on scorched-earth tactics. If you're interested in all the details (as well as the rest of WW1 in Africa), I'd recommend you check out The Great War in Africa by Byron Farwell.

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Lettow-Vorbeck's campaign consisted largely of rapid marches across the wilderness and regions with little European settlement punctuated by occasional ambushes of pursuing forces and scorched-earth tactics to deny the use of resources in the areas they passed through to the pursuing forces. In the absence of pack animals, they (as all participating armies in the region did) relied heavily on porters to carry their supplies that were often pressed into service. The tropical climate was hell on all involved, and attrition from disease and exhaustion took a huge toll on both Lettow-Vorbeck's troops and Entente forces. The scorched earth tactics Lettow-Vorbeck resorted to were certainly effective - it forced the significantly larger British forces pursuing them to rely on extended supply lines and huge numbers of porters as they couldn't rely on local supply - but it was certainly devastating to the local populations, who were either directly targeted (killed or pressed into service as porters) or indirectly impacted by the destruction of their homes and food supplies. Ultimately, the locals would suffer the most from the campaign, with some 350,000 civilians dying from famine caused by the campaign.

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Getting back to tactics and strategy, Lettow-Vorbeck's army relied on their movement to keep supplied. Apart from artillery pieces scrounged off of the cruiser Konigsberg that had been trapped in the Rufiji Delta and an abortive attempt to receive resupply via Zeppelin that was abandoned after British artillery forced Lettow-Vorbeck to abandon the landing site, the German troops relied heavily on supplies they had captured from enemy forces. They ventured south out of German East Africa and into Portuguese Mozambique, where they were able to capture a fair amount of supplies before being forced to withdraw north, and by the time Lettow-Vorbeck surrendered, his forces had been equipped with captured British rifles.

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Ultimately, the goal of the campaign was never really to defeat the British - given the scale of the forces they were against and inability of Germany to keep the colony from being cut off by blockade, significant conventional resistance wasn't feasible. In fact, authorities in German East Africa originally hoped to avoid conflict altogether. Lettow-Vorbeck's strategy was instead to tie down as many Entente resources as possible for as long as possible by evading them and constantly raiding so as to force the British to continue pursuing him. In that respect, he was spectacularly successful. A peak of a quarter million soldiers and 600,000 porters were tied down in East Africa, and the scorched earth tactics meant that further resources would have to be diverted for humanitarian needs. At the end of the war, although his forces had dwindled to fewer than 1,500 men, Lettow-Vorbeck had lunged out into Northern Rhodesia (modern Zambia) with every intention of bringing the war deeper into Africa.

There's something about the African theater in WWI that echoes the Thirty Years War, once described by C V Wedgewood :

no right was vindicated by its ragged end. The war solved no problem. Its effects, both immediate and indirect, were either negative or disastrous. Morally subversive, economically destructive, socially degrading, confused in its causes, devious in its course, futile in its result, it is the outstanding example in European history of meaningless conflict.

Sometimes I think fiction can capture meaningless conflict as well as a narrative history. Along with u/Meesus recommendation of Farwell, I'd like to add a novel: An Ice Cream War, by William Boyd.