When sending cryptocurrency you can choose how much you want to pay in fees in many wallets. If you send the high end of the daily average, your transaction will be processed quickly.
Meanwhile, if you choose something on the lower end, your transaction could be sitting around for a while before it gets processed.
Miners will generally mine transactions with high fees first, so you can pay them a little extra to expedite.
How much extra should I pay? Just pay the high end of the current average fee, assuming it is reasonable. See https://bitcoinfees.info for current average Bitcoin fees, use Google to find the current average fees of other coins.
Not all wallets allow you to adjust fees: Not all wallets let you control fees. For example exchanges tend to have their own methodology. This article only applies to situations where you have the option of adjusting fees (generally with wallets where you control your own private keys).
How long does a transaction take? Every blockchain is different, but with Bitcoin the quickest a transaction will be processed is 10 minutes. If you pay the high end of the current average rage, you are likely to in on the next block (so about 10 minutes for the first confirmation). If you pay lower, you could be waiting for hours… if you don’t include a fee or pay a very low fee, you could end up having your transaction rejected.
What is the current average fee? For more info on fees and the current average fees (i.e. what you should include in a transaction) see https://bitcoinfees.info. In general that site will show you next block, 3 block, and 6 block average fees. Each block takes about 10 minutes. So if you want your transaction to be processed within 10 minutes (likely, but not ensured), be safe and pay a little higher than the next block average.
Learn more about How Transaction Fees Work.