what exactly were the tactics used in areas where fighting was more mobile?

On the Eastern Front, infantry tactics in the beginning were based off pre-war training and ideas; the German infantry utilized fire rushes, while Russian infantry were trained to entrench and use cover wherever they dug-in. By 1916-17, the Russians and the Germans had moved towards a system based on Stosstruppen or 'shock troops', as demonstrated by the Brusilov Offensive, the German counter-offensives against the Kerensky Offensive, and the Battle of Riga.

How much did it resemble WWII?

With the exception of radios and submachine guns, WWI infantry tactics by at least 1916 were like those of WWII.

How did these tactics vary between different fronts?

The Austrians utilized Stosstruppen, and the Italians in many ways copied this with their Companies of Death and Arditi.

Also, with regards to trench warfare, how much of the fighting actually occurred in areas where trench warfare was dominant?

Fighting very much occurred on the Western Front from 1915-16, and on the Italian Front (though trench warfare is much too flattering for the fighting there). However, these were major offensives, especially in the West, which lasted weeks if not months, and often remained in the same sector of they front. Outside them, due to demands for guns, divisions, and shells, things would be relatively quiet.

When did use of trenches begin and end?

Slit trenches were used by soldiers on all sides from the beginning, essentially as fox holes. On the Western Front, it's generally dated to September, 1914, at the Battle of the Aisne, but I'd date it before that, just before the Marne when German and French forces in the south had already begun to dig in in the Vosges and the Argonne. As to when it ended, I've answered that [here] (https://np.reddit.com/r/AskHistorians/comments/3dxlav/what_were_the_conditions_during_ww1_in_the/ct9udmc).