Transmission Control Protocol/Internet Protocol (TCP/IP):

Nearly all computers today support TCP/IP. TCP/IP is not a single networking protocol – it is a suite of protocols named after the two most important protocols or layers within it – TCP and IP.
As with any form of communication, two things are needed: a message to transmit and the means to reliably transmit the message. The TCP layer handles the message part. The message is broken down into smaller units, called packets, which are then transmitted over the network. The packets are received by the corresponding TCP layer in the receiver and reassembled into the original message.

The IP layer is primarily concerned with the transmission portion. This is done by means of a unique IP address assigned to each and every active recipient on the network.
TCP/IP is considered a stateless protocol suite because each client connection is newly made without regard to whether a previous connection had been established.

CP/IP and the OSI Model Comparison
Let's Start by Comparing TCP/IP and the OSI Models. The TCP/IP model is basically a shorter version of the OSI model. It consists of four instead of seven layers. Despite their architectural differences, both models have interchangeable transport and network layers and their operation is based upon packet-switched technology. The diagram below indicates the differences between the two models:

Application Layer: The Application layer deals with representation, encoding and dialog control issues. All these issues are combined together and form a single layer in the TCP/IP model whereas three distinctive layers are defined in the OSI model.

Host-to-Host: Host-to-Host protocol in the TCP/IP model provides more or less the same services with its equivalent Transport protocol in the OSI model. Its responsibilities include application data segmentation, transmission reliability, flow and error control.

Internet: Again Internet layer in TCP/IP model provides the same services as the OSIs Network layer. Their purpose is to route packets to their destination independent of the path taken.

Network Access: The network access layer deals with all the physical issues concerning data termination on network media. It includes all the concepts of the data link and physical layers of the OSI model for both LAN and WAN media.

Transmission Control Protocol (TCP)
TCP is connection-oriented in the sense that prior to transmission end points need to establish a connection first. TCP protocol data units are called segments. The sending and receiving TCP entities exchange data in the form of segments, which consist of a fixed 20-byte header followed by a variable size data field.
TCP is responsible for breaking down a stream of bytes into segments and reconnecting them at the other end, retransmitting whatever might be lost and also organizing the segments in the correct order. The segment size is restricted by the maximum transfer unit (MTU) of the underlying link layer technology (MTU is generally 1500 bytes which is the maximum payload size of the Ethernet).
The image below shows the TCP segment format. The most important fields are explained further on.

Source Port and Destination Port fields together identify the two local end points of the particular connection. A port plus its hosts' IP address forms a unique end point. Ports are used to communicate with the upper layer and distinguish different application sessions on the host.

The Sequence Number and Acknowledgment Number fields specify bytes in the byte stream. The sequence number is used for segment differentiation and is useful for reordering or retransmitting lost segments. The Acknowledgment number is set to the next segment expected.

Data offset or TCP header length indicates how many 4-byte words are contained in the TCP header.

The Window field indicates how many bytes can be transmitted before an acknowledgment is received.

The Checksum field is used to provide extra reliability and security to the TCP segment.

The actual user data are included after the end of the header.
User Datagram Protocol (UDP)
UDP protocol consists of fewer fields compared to TCP. The reason for that is because certain data types do not require reliable delivery and extra overhead. Real-time traffic for example, needs to be transported in an efficient way without error correction and retransmission mechanisms.
UDP is considered to be a connectionless protocol. It leaves reliability to be handled by the application layer. All it cares about is fast transmission. The UDP segment format is presented in the diagram below:

How does TCP/IP work?
The TCP/IP protocol is designed such that each computer or device in a network has a unique "IP Address" (Internet Protocol Address) and each IP address can open and communicate over up to 65535 different “ports” for sending and receiving data to or from any other network device. The IP Address uniquely identifies the computer or device on the network and a "Port Number" identifies a specific connection between one computer or device and another (i.e between two IP Addresses). A TCP/IP "port" can be thought of as a private two-way communications line where the port number is used to identify a unique connection between two devices. The concept is very similar to any other type of port on your PC (serial, parallel, etc) except that instead of having a physical connection, the TCP/IP protocol creates a "virtual IP port" and the network hardware and software is responsible for routing data in and out of each virtual IP port.

TCP/IP Client and Server Connections
TCP/IP connections work in a manner similar to a telephone call where someone has to initiate the connection by dialing the phone. At the other end of the connection, someone has to be listening for calls and then pick up the line when a call comes in. In TCP/IP communications, the IP Address is analogous to a telephone number and the port number would be analogous to a particular extension once the call has been answered. The “Client” in a TCP/IP connection is the computer or device that “dials the phone” and the “Server” is the computer that is “listening” for calls to come in. In other words, the Client needs to know the IP Address of whatever Server it wants to connect to and it also needs to know the port number that it wants to send and receive data through after a connection has been established. The Server only has to listen for connections and either accept them or reject them when they are initiated by a client.
Once a connection through a TCP/IP port has been established between a TCP/IP client and a TCP/IP server, data can be sent in either direction exactly the same way that data is sent through any other type of port on a PC (serial, parallel, etc.). The only difference is that the data is sent across your network. The connection between a Client and a Server remains open until either the client or the server terminates the connection (i.e. hangs up the phone). One extremely nice benefit of the TCP/IP protocol is that the low level drivers that implement the sending and receiving of data perform error checking on all data so you are guaranteed that there will be no errors in any data that you send or receive.