Short answer
The base fee is 0.000005 SOL per signature, a tiny fraction of a cent. Optional priority fees can be added to get included faster when the network is busy.
Every Solana transaction pays a base fee per signature, which is very small. During busy periods, wallets and apps add a priority fee to move up the queue, which can raise the cost to a few cents, occasionally more.
The first time you hold a new token, Solana also needs a token account for it, which requires a small refundable deposit called rent, roughly 0.002 SOL. You get it back if the account is closed later.
These network costs are separate from any app fee. On DYOR, the app fee is a flat 0.5% per trade.
See the checks for yourself
18+ only. Self-custodial: you keep your keys. 0.5% per trade, no minimum. Memecoins can go to zero.