How do you manually construct packets. Get a vampire and clamp it onto your network cable, then start sending electronic pulses down it (on and off) in the right sequence to build a packet.

Your question is to vague. What operating system, what type of packet, what is it's use. There are several packet builders out there for every OS... the one that S3cur|ty4ng31 mentioned is decent for Windows, there are also several other ports.

At the heart of the question though, the most likely approach that you will take is to learn a programming language. Learn c, c++, or some other language and create your own packets using the built in libraries and headers. It takes a lot of work, but at least you are doing it yourself.

Since i'm guessing this is another one of those questions from which no good can come, you will go with the first suggestion and download a canned packet builder.

Like Relyt said go out and learn something. Learn about Data, Segments, Packets, Frames and Bits, and how the OSI model relates to those. How do you know it's a packet you want to build and not a frame or a segment? Do you even know the difference? Go read a book, do some learning and search for your own solutions instead of trying to take the easy way out.