You always need to dig a bigger hole than the plant but depth depends on the plant. Which ones are you planting?

If the part where you want to plant climbers is an area which hasn't been touched for a long time, or dug over, best to dig it over and add some soil conditioning compost, the whole area, and then make your planting holes for climbers a few days later. Can't be specific about planting depths, etc., as DRC says, depends on what you're buying.

Most should be planted at the same depth as in the pot except for Clematis which should be planted 3 inches deeper. Don't plant too near the wall (if that's where they are to climb) but plant a foot away and lean the plant towards the wall. If against a fence, I staple bean and pea netting to it to give the plants something to climb up. From a few feet away it is almost invisible.

One good rule of thumb, though, is to plant plants from containers no deeper than they were in the container.

Is that so for Clematis Tuqb?

Not certain, since we don't do much clematis here. I wouldn't, because the plants that seem to survive deep planting the best are those that form adventitious roots easily, such as willows, tomatoes, etc. All of the garden gurus that I know always say to never, ever plant more deeply than in the container, though you can often get away with putting something coarse and porous around the stems after planting, such as ground bark, or coarse gravel.

We plant Clematis below the level of the soil. But I am not sure if that applies if planting an established one from a pot?

I plant clematis either on their side, or 4 inches deeper than they were in the pot - on their sides, encourages more shoots off the roots, 4 inches deeper does the same thing. Not necessary with species clematis though.

Thanks Bamboo

Thanks from me too, Bamboo!