I understand how to draw chair form for trans-decalin (figure 1) for the usual structure, but I am having difficulty if taken as shown in figure 2 wherein the hydrogens at bridge-head carbons are in opposite orientation. Please help me with relevant chair form diagram.
Use of 3D models
3D version of Figure 1:
Viewed upside down (rotate about z by 180 degrees):
Now it looks like we are viewing from the bottom, so we will turn the molecule a bit around the x axis:
Use of 2D projections
If you want to use the 2D projections, consider whether hydrogens are pointing up or down on the bridge head. First, we will interpret the chair as viewing the top of the ring from above (left panel) rather than viewing the bottom of the ring from below (right panel) to avoid ambiguity.
No matter whether you use two fused chairs as drawn by the OP (Fig 1 bottom panel) or its mirror image, the front hydrogen will point down and the back hydrogen will point up. This works well for Fig 1.
In order to use the same chair building block but show the front hydrogen pointing up, you could rotate the flat model, and connect two chairs accordingly, as shown below. In effect, you choose the location of the two bridging position to match the stereochemistry you want.
A common notation in crystallography used for denoting atoms above and below the plane of the paper for the structures with quasi-flat overall shape is the use of filled (⚫) and open (⚪) circles, respectively. I think you can use this technique for decalin as well. For trans-decalin with both rings in chair conformation there is even no need to change your drawing for pseudo-3D (red plane refers to the plane of drawing, not symmetry) (scheme A).
Also, note that in crystallography there are also plus (+) and minus (−) signs used for the same purpose, e.g. denoting an object (including atoms) that lies above and below the plane containing the reference axes, respectively. I personally find this notation less applicable here because of the possible confusion arising with the clash of notation for charge distribution (scheme B).