This is not the most inexpensive option for hiking because the trail is inside Yosemite National Park. There is an admision fee. However you may be able to minimize the fee by bringing a friend in the military with you in the car, veteran, or senior citizen. If you are planning on going frequently you may want to consider buying an annual pass. If you are a senior citizen you might want to purchase a senior citizen pass.
Half Dome is extremely technical because a significant portion of the trail requires one to use cables. The cables are often very very very icy, especially in the early morning. However if you go later to avoid the ice you may be stuck in traffic going up the mountain. This can be very challenging particularly when people are going up and down and trying to pass each other on the cables. Additionally because of the challenge of cables once you start up it is almost impossible to go down. The entire hike is about 16 miles. The hike brings you over 4,000 feet above the Yosemite Valley. The trail includes out of this world views of the Yosemite Valley in addition to the High Sierra area. You can see the Vernal and Nevada Falls.
Make sure to bring layers because there is vast temperature changes as you are going up the mountain. Also you may get hot on the first two hours of the hike because it is extremely steep heading up towards the vernal falls view.
Make sure to get a permit before going. Plan extra time in case of delays at sub dome. Also consider making a climbing harness or bringing a harness to clip onto the cables. It can help you get a good grip, especially when you are going later and may have people above you slip.