Even though there are countless variations on the structure of a yagya, in general they being with Ganesha puja (to remove obstacles to the successful conculsion of the yagya), then the kalasha puja (to bless and purify the water contained in the water pot), and then a series of pujas, the specifics of which will vary depending on the type of yagya being performed.
In most cases, the offerings follow a sequence that is similar to inviting a guest into your home. The deity is offered a drink, some new clothes, flowers, water, food, etc. In the photo above water is being poured over the lingam after it has been decorated with offerings of cloth and flowers.
Even offerings of food are placed on the lingam, the feeling being that the deity “consumes” the essence, leaving the material form of the food to be consumed as prasadam.
The offerings proceed and can at times be quite extensive. In some yagyas it can be well over 100 different items.
The leaves of the bilva tree are frequently used in Shiva pujas, particularly during Shivaratri. In the photo above we see some sandalpaste being poured over the Shivalingam which has been adorned with a bilva leaf.
You can see some of the milk drain away from around the lingam. The yellow liquid that is mixing with the milk is most likely turmeric, or sandlwood.