Yes you can. Depending on the institution you are attending and/or the type of training you are receiving. In most cases, you will have to be enrolled in less then 10 credential hours of classes to still be considered for unemployment. Main thing here is to show that you are still available to receive FULL time work if offered. You will be scheduled for an interview by an unemployment representative, but the best thing to do is call them ASAP to answer these questions. The scheduling for questioning regarding your training/schooling, usually has a one month wait period, so if you need your check fast, you will not get it till after their questions are answered.
If you file a claim and indicate you are attending school, you will be asked the days and hours of your classes. You will be asked if you are able and available for full time work outside of school hours. Usually, claimants are. You can indicate you work at night and on weekends. There are all kinds of different schedules today. So, yes, you can usually collect uc while attending school. You have to make sure you tell the uc office that you are able and available to work also. On the other hand, if you quit a job to attend school, 99% of the time you will be ruled ineligible to receive benefits.
In some states there are programs that allow you to attend school full time and still get benefits. If you are going to school for a high demand occupation you may be able to draw benefits until graduation especially if your company is prone to many layoffs. Ask at your local office or do an internet search on your states unemployment website. I know Iowa has 2 programs that help.