Don't hide the ball. In most jurisdictions an attorney-client privilege exists during the intake process to protect and promote a candid discussion. One of the first things you should do is explain is what type of attorney you are looking for, how you envision the payment structure (don't need to discuss numbers at first), and where the case is. For example, you should say, I'm thinking about exploring my legal options against my former employer and need a contigency based counsel. Right away, you've communicated quite a bit and if the attorney does not handle contigency matters or employment matters it will be a quick call. If you already have an attorney on the case and are thinking about switching, tell the attorney that up front as well. (Additional questions asked will be does your current counsel know you want to switch? Will their be a lien on the file?) Also, if you've already lost the case and looking for an attorney on appeal, that should be the first thing mentioned.
This is the most efficient way to proceed and you will be able to listen to the lawyer's skill in directing the conversation and they will flush out the facts they think are important to make a determination.
Time is money for both you and your lawyer. If you tell a long-winded story in novel format, the lawyer will cut you off and try to re-direct you regarding the substantitive facts of your case. Some people try to talk with counsel like they are gossiping with their friends and start cursing or wandering from topic to topic. We understand that the matter may be very personal to you and there are emotions involved, but during the intake the lawyer is also making conclusions regarding how you will be a witness and if you are unfocused and/or coarse the lawyer and/or extremely difficult, the lawyer may pass on the case because he may not think you will be good during your deposition or trial or does not want to deal with the added aggravation of a difficult client.
Imagine walking into a doctors office and telling him or her that you want a butterfly incission to go in and explore the kidneys and then perhaps the gall bladder and during the exploratory process you want your appendix removed. Explain the facts to your lawyer and let the lawyer decide the law. There are many things you may have read online or seen in theater that don't functionally translate to the way law is actually practiced. Just because you've discovered a wonderfuil obscure statute doesn't mean its enforceable or tactically sound. Also, if the lawyer thinks you want to be quarterback or will be an armchair quarterback it may fall into the too high maintanence catergory and you will be declined.
During the intake process, please make sure you include all important facts, even if they are hurtful as that will help the attorney accurarely assess the case. If you indicate you don't know why you were fired and the attorney commences an action and it turns out that they had video that you knew about of you smoking crack in the breakroom, and your complaint based on your intake says fired without cause, that will be fatal to the case and the Court in its discretion can impose a fine on you. Don't put yourself and your attorney in that position and let them know the weak parts of the case as well.
What do you have to back up your claim? In an injuury case it may be a police report. In an employment case its especially important because a lawyer will elevate written proofs and discount what you think other people will testify to.