-Talk crap about the father. Not in court, and DEFINITELY not to your kid. Like "your daddy didn't send your shoes back with you? What a frickin' *sshole" etc.
-Put your kid in the middle of fights or discussions that should be between you and the ex. Like don't say to your kid "would you rather go to daddy's or stay with mommy?" or "i'm mad at your dad so he can't see you this week" or "can you ask your daddy when he's going to pay me child support/ call me/ sign school papers" etc.
-Say things like "your daddy has a new life and doesn't care about you/us" etc.
-Make it difficult for him to get ahold of your child, by changing your phone number/address or not picking up the phone.
These things can get you in trouble with the court and make you lose custody, they are examples of parental alienation, which basically means you are brainwashing your kid against the other parent. It is considered a form of child abuse because you are deliberately trying to turn your child against him.
When you are in court AVOID talking about what a bad father he is, how he has this or that issue, or doesn't come see your daughter. Focus instead on why YOU are the best thing for your child, how you care about HER well-being and that you believe it is in her best interest that she stay mainly with you. Courts are used to hearing couples bad-mouth each other and take it all as hearsay. They are interested in hearing what is best for the child.
If it is what is best for your child and the father really has had little involvement till now and you can prove those points you will most likely win a custody case. Keep in mind that you will most likely NOT be granted "sole custody". This means that you and you alone make decisions regarding your child (school, medical, religious, etc) and the other parent has no say in the matter. Courts only grant sole custody if the other parent is abusive, mentally incompetent, or something similar. The best you can usually hope for is joint custody with you as the primary caregiver. This means you have physical custody (she is with you most of the time) and her father has visitation rights.
It is a long process and if you fight about it, things only get longer and harder. The best thing you can do is try and settle the matter out of court, if you can, with legal papers drawn up. It is in the best interest of your child for her parents to get along when it concerns her, as best you can.
Note about input from lady above me: the only reason a court will require supervised visitation is if there is a reason, ie abusiveness, drug use, mental issues, neglect, etc. Like Britney Spears locking herself in her bathroom with her son with the cops outside and then going crazy and shaving her head. Otherwise it will just be normal visitation.
You can check to see if the attorney is listed in Martindale-Hubbell which is one of the older established listing services for attorneys. Their website http://www.martindale.com/home.aspx allows you to search for attorneys by practice area and location. Martindale also has a voluntary rating system, based on peer review, rating lawyers by accumen (A B or C) and also may include an ethics rating (V for high ethics rating). Martindale also has a voluntary client review system. While both to a degree are somewhat self-serving because they are voluntary, there are some objective standards such as minimum number of years of practice required for each rating, and it generally does still require that the lawyer have enough experience working with other lawyers, judges and clients to have gathered enough contacts in the field to have a peer group and client base that holds them in regard.
On the flipside, you can check to see if there is any reason to be wary of an attorney you are considering by checking his or her record with the local and state bar association to see if there have been any complaints filed. Again the mere presence of a complaint or complaints is not necessarily indicative of a bad attorney as some clients simply file a complaint when they are not satisfied with the outcome of their matter even if the attorney bore no fault in the result but it is something you can consider when evaluating an attorney for possible representation of you for your matters.