Lemongrass

It has lemon in its name and is not a citrus, and it is not something you juice. Use the pale base, bruise it, and in most dishes take it out before serving.

It is not a lemon

Its aroma compound (citral) overlaps with lemon peel, which is why it smells the way it does — but there is no acid in it. Used in place of lemon it will not make anything sour, and lemon cannot imitate it in the other direction. If you need acidity, add lime separately (lemon).

The part you use is the pale base

The firm white-to-light-green bottom 10cm — the aroma lives here.
The green tops — tough and weakly flavoured. Do not bin them; put them in stock.
Peel off the one or two dry outer layers.

Bruise it before you use it

The aroma is locked inside the fibre. Whacking the stalk with the back of a knife or a rolling pin ruptures that fibre and lets the aroma into the liquid. A whole stalk simmered untouched gives up less than half of what it has.

In broth — bruise, cut into 5cm lengths, fish them out at the end. This is tom yum goong and laksa.
In curry paste — slice it as thinly as you can, cutting across the fibre, then pound or blend. Cut coarse and you will feel the threads. Green curry.
In marinades and grilling — mince it fine. Something like lemongrass chicken needs it fine enough to reach the meat.

Know which pieces are eaten and which are removed

Lengths of stalk are not eaten. No amount of simmering softens that fibre; treat what went into a broth like a bay leaf and take it out.

Finely minced or pounded lemongrass is eaten. Those are two uses of one ingredient, and when a recipe says only "2 stalks lemongrass" the method tells you which — broth means remove, stir-fry or marinade means eat.

Dried and frozen

Frozen — holds its aroma well. Cut into 5cm lengths, bruise, freeze; good for three months or more, and used straight from frozen (freezing and thawing).
Dried — much weaker. Usable in broth, not really enough for a paste. Roughly one fresh stalk ≈ 1 tsp dried.
Tube and jarred pastes — acidity regulators change the aftertaste. An option when there is nothing else.

Substitutes

There is no accurate one. The nearest approximation is a little lime zest with a little lemon zest, which gets the direction and not the grassiness.

Storing

Two to three weeks refrigerated, wrapped in paper in the vegetable drawer.
Stand the base in water and it will root; potted, it grows.