Check for any exemptions to the visa limits provided by your degree or area of expertise. For example, 20,000 foreign nationals holding master's degrees or higher, from U.S. universities are exempted from the visa cap each year.
Seek corporate sponsorship for your visa as early as you possibly can, before graduation if you are able to. Taking curricular practical training during your degree course may help introduce you to potential employers willing to sponsor you. You should try and find out whether they are willing to sponsor you for your green card application while employed. If they won't, you may be unable to follow that path, meaning you may only work a maximum of six years in the United States before having to leave.
Consider, if you are having difficulty finding a sponsor, whether you should apply for an H1B visa immediately upon graduation, or seek to take up an opportunity for optional practical training in the meantime. This would enable you to gain practical experience to add to your academic qualifications, which may be attractive to potential employers and widen your options. Graduates are entitled to apply for OPT for a maximum of 12 months. During this time, you can still apply for transfer to H1B status.
Make sure you allow enough time for the visa process to take place. There are set times of year for applications to be made and the process can take several months. If you are not going the OPT route, you only have 60 days from the end of your F1 visa to obtain change of status.