佔 for to occupy or take up. 占 keeps its older sense, to divine.
A crack 卜 above a mouth 口 — the diviner reading aloud the split that appeared in a heated turtle shell. That is the original sense, zhān, to divine. Read zhàn it means to take and hold, which is the meaning almost every modern word uses.
占 carries both halves of its history. 占卜 is still fortune telling, while 占领 is to occupy militarily and 占用 is to take up space or time. 占便宜 — to occupy the advantage — is the everyday accusation levelled at someone who takes more than their share.
A crack in a shell 卜 above a mouth 口 — the diviner reading the omen out loud.
卜 on top is a literal picture: the crack that opened in a heated ox bone or turtle shell. Reading those cracks is how the oracle bone script — the ancestor of every character here — came to be written down.