Choose a date for your climb. Decide if you'll do the climb in a single day or will stay overnight. Determine how many people will participate in the climb.
Secure a permit for the climb. Permits to climb Mt. Whitney are issued by the federal government in a lottery system. You'll need to complete an application detailing the information you assembled in Step One and submit it, along with the application fee. Application for the lottery must be made by the end of February each year. If you miss the February deadline you may still apply; these late permits are issued on a space-available basis only.
Train for your climb by bicycling, climbing stairs, running, or engaging in other prolonged aerobic activity several times a week. Some people like to train wearing the pack they'll wear on their climb. Begin training as soon before your trip as you can: two weeks before is good, six weeks is better, three months is great.
Assemble your gear. For a day trip you'll need to plan on carrying at least a gallon of water per person, lunch and snacks, rain gear, a head lamp in case you get caught out after dark, and a jacket, hat and gloves, since even in summer there can be storms and snow at the top of the mountain. You'll need a sturdy, comfortable pack in which to carry this gear. Wear supportive hiking boots. If you buy new boots, wear them on local hikes several times before you make the climb to break in the boots and prevent blisters. Wear wool or synthetic socks made for hiking, sunblock and a hat to protect against sunburn. Pack a first aid kit. Many people find trekking poles help make the climb easier. Mt. Whitney has a hiking trail to the top, so you won't need technical gear.
Do a test climb of a smaller peak or two. This will allow you to get comfortable with the gear and test how you handle altitude.
Arrive at the town or campground you're using as your base a day or two early. Take some high-altitude drives and get out and walk around. This will help you acclimatize to the altitude.
Eat a high-carb dinner the night before the climb and get plenty of rest.
Start early. Many hikers start at 3, 4 or 5 a.m. and hike the first section of the trail by headlamp. This gives you plenty of time to get to the top and back. According to the Mount Whitney Day Hiking Page, most people spend between 11 and 17 hours making the round trip up the Main Trail and back.