I just received my tax return from the company I worked with all of last year. I am not employed with them anymore and am looking to file my taxes. According to the company I was an independent contractor, and therefore have to file a 1099-Misc, which is the form they have sent me. During my employment with them I was told that there are certain deductions that I can claim when filing my return. Among these items were all work-related things such as laptop, cell phone, and transportation to and from multiple business locations throughout my assigned counties. Is this correct? Am I safe to claim these expenses as deductions as they were for use during my employment with the company? Any advice would be greatly appreciated. Thank you!

First YOU file a tax return, not the company and you RECEIVE a 1099 not file one.

That being said, you can complete Schedule C of your return and claim the amount of the 1099 there along with any expenses incurred while earning that money.

On your tax return, you report 1099-MISC income on schedule C. You can deduct business related expenses. You can deduct some amount for laptop based on business use and personal use and period used. So deductions for laptop and cell phone are not just a simple as it appears.
Also commuting miles are not deductible. One location to other location are deductible. You need proper record for that.
Your income form schedule C is subject to SE tax at 15.3%.