Yes, if it is not self-employment income, need the T2200 form from your employer.
Many employers are very hesitant to provide this, if they provide any sort of flex / random touch down office space that the employee can use at least half the time. Essentially they are declaring that it is a requirement of employment that the employee provide their own working office more than half the time.
What can you claim?
To see what expenses are allowed to be claimed by employees, after they have a T2200: Form T777.
The key items are car use between office locations if not reimbursed, supplies, and use of home office in the % that is not personal use (utilities, maintenance), and "other" such as installing a second office line, or increasing your internet capacity..
IMO, It is not as generous as for self employment (no mortgage interest deduction but if you rent you can claim a portion of your rent) , and likewise to self employment income, can not be used to create a loss by claiming these expenses, only carry them forward..
Example - How much is it worth to you?
My example, the home office is used for a part time employment job, 10% of my home is the office, and 20% of the time I use it for another business purpose not covered by a T2200. I can claim only 8% of my home: Insurance + utilities + basic maintenance; PLUS all the supplies (markers, binders, printer paper) that is consumed plus all of the the extra home line I have added just for this employment. I estimate I can claim 8% x $5000 = $400 per year.
I honestly don't know how one would claim equipment (cell phone purchase, laptop), except that perhaps the employer is required to reimburse you directly for those costs, as they are not supplies.
$400 per year x marginal tax rate (assume 30%) = $120 tax reduction. In other words, not a large amount for me. People that need to drive from home office to other office / work locations may be able to claim more, or if your office is a large portion of your home (full basement, perhaps).