It can take a few weeks to a few months, depending on how dry it was and what type or species of wood it is.
It has to become waterlogged to sink. You can speed that up by weighting it down or tying a weight to it to submerge it completely, but it can still take quite a long time to sink to the point it will stay down and stay put by itself.
Grapevine, for example, can take quite a few months to sink, I know someone with a piece that took nearly a year to sink entirely. The wood pieces often sold for reptile terraria may take months to sink too, they are less dense even when waterlogged. The dark brown 'driftwood' sold in LFS
's usually will sink within a day or two unless very dry and a small piece. Mopani wood usually sinks immediately, it's extremely dense and heavy even when dry.
One thing you can try if the piece is small enough, is boiling it for a few hours. That will soften the wood fibres a bit on the outside and help water penetrate a bit faster. But in the end, patience is the key.