One of the first things that a woman should do in order to maintain a good relation or rapport with other women, is to be nice to other women. Being nice basically involves treating other women with respect, not talking trash about them behind their backs, not thinking or planning mean or evil things about them, and helping them in their time of need.
Do not be over-judgmental. Women tend to judge each other on a lot of things. This is due to their habit of over-analysing things that other women say or do. This often results in misunderstandings and the misinterpretation of intentions. A lot of women have admitted that they prefer to have male friends over female friends because the former are not as judgmental as the latter. In order to get along with other women, you should stop judging them.
Rather than competing with other women all the time, put yourself in the same boat as them. By creating a feeling of solidarity with other women, you will be able to form a stronger bond with other women such as your class-mates or female colleagues.
Look for females that share some of your interests; you will find it easier to become and stay friends with them. You will have plenty of things to talk to them about and plenty of hobbies to participate in together.
Show your confidence in other women by asking them for their opinions while working on a project with them, shopping for clothes or shoes, deciding a menu for a party, etc. Asking your female friends and acquaintances for their opinion will make them feel valued and thus make them fonder of your company.
If you have a problem with a particular woman, do not go around sharing it with others. The best thing to do is to approach her directly and talk it out with her. She will surely prefer to have you discuss the issue with her directly, instead of dragging other people into it.