Grading and surface drains
Soil is shaped to fall away from the house, and surface inlets are added where water has nowhere to go on a flat lot.
Foundation movement is a moisture problem before it is a concrete problem. Getting water away from the house, and keeping a big tree from drinking out from under it, is often the cheapest thing you can do.
Arlington gets wet springs and dry summers, and clay reacts to both. Damage usually comes from one part of the ground being much wetter or drier than the rest, which is exactly what bad grading, a broken gutter or a thirsty post oak produces.

The aim is boring and consistent: keep the soil around the whole house at roughly the same moisture, all year.
Soil is shaped to fall away from the house, and surface inlets are added where water has nowhere to go on a flat lot.
A perforated line in gravel intercepts water moving through the soil toward the foundation and carries it to a sensible outlet.
Roof water gets taken well clear of the slab instead of soaking the same corner every storm. Simple, cheap and frequently the whole fix.
A vertical barrier set between a large tree and the house stops roots pulling moisture out of the clay under the slab, without taking the tree down.
The other half of moisture control costs nothing. In a long Texas drought, soaker hoses run around the perimeter of the house on a regular schedule keep the clay from shrinking away from the slab edge. Little and often beats a flood once a month, and the hose should sit a foot or so out from the slab rather than right against it. Our guide to watering your foundation goes through it properly.
Trees are a judgment call. A mature post oak or live oak is worth keeping, and a root barrier is usually a better answer than removal. Removing a large tree that has been drying the soil for thirty years can cause its own movement as the ground takes water back up.
If the house has already dropped, drainage alone will not lift it, and you will want slab repair or piers as well. A measured inspection tells you which situation you are in, and the fix now or wait guide covers the timing question.
The length of drain needed, how much digging the lot requires, whether there is anywhere to discharge the water, and whether existing hard surfaces have to be crossed. A few downspout extensions are a small job; a French drain around two sides of a house is not. Ask for a quote after the provider sees where the water goes.
It stops the cause, it does not undo the effect. If the house has already settled, the cracks stay until the structure is lifted and supported. Drainage is what keeps a repaired house from going the same way again, and on a house that has only just started moving it can be enough on its own.
Usually not as a first move. A root barrier between the tree and the foundation addresses the moisture without losing a mature tree, and removing a large tree can cause the soil to swell as it takes water back. Get it looked at before you call a tree crew. See what an inspection covers.
When you call, mention where water stands after a storm and how close the trees are.