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Figure out why they rejected you. Think over your current relationship. Examine your approach. Respect their answer. Be patient.
This can be difficult because you don't want to seem desperate or overly hurt, but if your crush didn't give you a good answer as to why they didn't want to go out with you, it could be good to meet up with them and ask a few questions to gain some insight as to what they are thinking.  If they very bluntly stated why they didn't want to go out with you, like "I'm not interested in you for this reason" or "I'm going through something difficult and don't need the stress of dating," then you don't want to irritate them by asking for more explanation. People are often caught off-guard when asked out, so a lot of times they come up with an answer on the spot that may not be the complete truth. Calmly approach your crush and ask them if they wouldn't mind grabbing coffee (not as a date) because you wanted to talk through some things with them. Then, when you are together, ask if there was a specific reason they didn't want to go out with you or if your approach was what turned them off. Do not then proceed to ask them out again, but thank them for giving you some insight and be understanding and be patient. Sometimes it's the essence of the relationship that is what caused the rejection. Are you asking out your best friend and they are worried that it will ruin the relationship? Have there been conflicts recently that have left your crush confused or irritated with you? Thinking through your relationship can be helpful to know if it was part of the reason you were rejected.  If you asked out someone you met once at a party or on a night out, this doesn't necessarily apply to you, but if you asked out a good friend it's possible that they don't want to ruin your relationship or there's something else going on in their life that's keeping them from jumping into something new. It's also possible that at this point they just aren't attracted to you, which in that case it just takes time and patience before you can ask them out again. Did you just ask someone out that you didn't know in a very demeaning manner, were you confident or really nervous in your approach, or did you catch your friend off guard and they didn't know how to respond? If you have asked other people out, think about the approaches that were successful and those that weren't and think about how you came across to your crush. If you asked someone out and were rejected, don't insist on taking them on a date. It can seem desperate and be incredibly annoying to your crush if you persist when they've already told you no. Once you have figured out why they rejected you, respect their answer and don't ask them out again right away. As previously stated, you want to respect the person you asked out by giving them time. Sometimes people need to process and think over things, and over time they may realize that they are interested in you. Giving your crush space to think over their feelings towards you could lead to a much more positive answer later on.