Can you see clearly right after a corneal transplant?

No. With the new partial thickness transplantation technique (dsek), the vision is very poor for the first 2 days as the air bubble in the front of the eye interferes with vision. After this, the vision returns relatively quickly so long as the transplanted tissue is healthy and swelling dissipates, usually 2-12 weeks.
Better, Not Clearer. Many patients i perform transplants on, whether it's a partial thickness, sutureless, or a full thickness, sutured transplant can see better than they could before surgery. Depending on the pre-surgical vision, and on the diagnosis, many patients are seeing better and brighter than they could before. Realize though, it may take weeks or even months for some patients to say it is "clear".
Usually NO. Most corneal graft patients have an extended post-op period of some blur as the tissues mend and heal. Please be patient.
Not usually. Although it is possible to have good vision immediately after surgery, it normally takes 6-12 months to get to the best vision postop.
Not immediately. Depending on the type of transplant visual recovery can take anywhere from 3-12 months.
No. The transplant needs time to heal in many ways. The new cornea needs to become epithelialized (new surface) from the recipient. Also, corneal edema (swelling) needs to resolve. Lastly, there is often a high level of astigmatism that needs to be deal with by selectively removing sutures, and using prescription glasses or a rigid gas permeable contact lens.