The basic questions that need to be answered are (1) your status as Resident /Non Resident and (2) your relationship with the employer.
If you are working from India, you will be resident and you will be liable for tax on your global income, including the income earned in USA. You can claim double taxation relief, if you had to pay taxes in USA also.
If your relationship with the US company is that of Employer and Employees, you will be still assessed under the head : Salaries. The tax situation will be the same, except changes in the emoluments. However, tax has to be deducted by the US company.
If your relationship with the US Company is that of a service provider as a professional, your income will be assessed under the head: Income from business or profession. In such case, all reasonable expenses incurred in connection with the earning of your professional income will be allowed as deduction in computing your taxable income. You will be able to claim deduction on account of depreciation on your assets employed in your profession, such as Laptops, Mobile, vehicle. The other expenses like travelling and conveyance to the extent they are not reimbursed by your firm/client can also be claimed. In addition regular expenses such as your expenditure on books, vehicle maintenance and communication expenses can also be claimed.
If your professional income exceeds Rs 25 L, then your accounts will have to be audited by a CA.