PPP Negotation Trace for one of my internet connections (Earthlink - uunet node):
 
#1. We Send LCP Request
FF 03 C0 21 Header FF/03=ADR, C0/21=LCP
01 00 00 06 01=LCP Req / 00=id / 00=size hi / 06=size low(6)
07 02 07=Protocol compresison.  Informs other end we allow protocol field in non LCP packets to be compressed to one byte from two.
64 7B PPP Checksum;
#2. We receive an LCP Request
FF 03 C0 21 Header
01 01 00 1B 01=LCP Req / 01=id / 00=size high / 1B=size low (27)
01 04 05 F4 01=MRU / 04=size / 05F4=Min Receive Unit size (1524)
02 06 00 00 00 00 02=ACCM option / 06=size /  00000000=no characters sent need escaping
07 02 07=Protocol compresison / 02=size  Other end allows protocol field in non LCP packets to be compressed to one byte from two.
08 02 08=Address and Control compression / 02=size (Informs us the other end allows the FF 03 to be eliminated in a packet)
13 09 03 00 C0 7B 70
5D C1
13= / 09=size 
20 4A PPP Checksum
#3. We send an LCP REJ(for #2)
FF 03 C0 21 Header
04 01 00 1D 04=REJ / 01=id / 00=size high / 1D=size low(20)
13 09 03 00 C0 7B 70
5D C1
Reject this option
2D 0E PPP Checksum
#4. We receive an LCP Ack (for #1)
FF 03 C0 21 Header
02 00 00 06 02=LCP Ack
07 02 Echoing back our options...
19 77 PPP Checksum
#5. We Receive a new request without the option we rejected in #3
FF 03 C0 21 Header 
01 02 00 12 01=Req / 02=id / 00=size high / 12=size low(18)
01 04 05 F4 01=MRU / 04=size / 05F4=Min Receive Unit size (1524)
02 06 00 00 00 00 02=ACCM option / 06=size /  00000000=no characters sent need escaping
07 02 07=Protocol compresison / 02=size  Other end allows protocol field in non LCP packets to be compressed to one byte from two.
08 02 08=Address and Control compression / 02=size (Informs us the other end allows the FF 03 to be eliminated in a packet)
D6 5D PPP Checksum
#6. We send and LCP ACK (for #5)
FF 03 C0 23 Header FF/03=Adr C0/23=LCP PAP
02 02 00 12 02=Ack / 02=id / 00=size high / 12=size low(18)
01 04 05 F4 Echoing the options from #5...
02 06 00 00 00 00 ...
07 02 ...
08 02 ...
EE 5C PPP Checksum
#7. We send an IPCP request for an IP of 0.0.0.0
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
01 01 00 0A 01=Req / 01=id / 00=size high / 0A=size low(10)
03 06 00 00 00 00 Request IP of 0.0.0.0
13 28 PPP Checksum
#8. We recieve an IPCP request
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
01 01 00 10 01=Req / 01=id / 00=size high / 10=size low(16)
02 06 00 2D 0F 01 02=IP protocol compression / 06=size / 002D=Van Jacobson Compressed TCP/IP headers / 0F=Max-Slot-Id / 01=Comp-Slot-ID
03 06 CE 73 98 07 Host IP is CE.73.98.07
28 C0 PPP Checksum
#9. We reject an IPCP option (from #8)
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
04 01 00 0A 04=Rej / 01=id / 00=size high / 0A=size low(10)
02 06 00 2D 0F 01 Reject IP protocol compression (we got enough to worry about already!)
86 DE PPP Checksum
#10. Our IP of 0.0.0.0 was rejected (from #7) but we get an IP suggested
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
03 01 00 0A 03=Rej / 01=id / 00=size high / 0A=size low(10)
03 06 3F 1B 38 3D IP of 3F.1B.38.3D is suggested
61 B0 PPP Checksum
#11. Send new request requesting the suggested IP
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
01 01 00 0A 01=Req / 01=id / 00=size high / 0A=size low(10)
03 06 3F 1B 38 3D request IP of 3F.1B.38.3D
2F E8 PPP Checksum
#12. Receive a new IPCP request with the option we rejected (in #9) removed
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
01 02 00 0A 01=Req / 02=id / 00=size high / 0A=size low(10)
03 06 CE 73 98 07 Host ip again is CE.73.98.07
11 A7 PPP Checksum
#13 We ack his new request (from #12)
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
02 02 00 0A 02=Ack / 02=id / 00=size high / 0A=size low(10)
03 06 CE 73 87 07 Host ip
78 D3 PPP Checksum
#14 We receive an ACK for our request
FF 03 80 21 Header FF/03=Adr 80/21=IPCP
02 01 00 0A 02=Ack / 01=id / 00=size high / 0A=size low(10)
03 06 3F 1B 38 3D Our IP of 3F.1B.38.3D confirmed
46 9C PPP Checksum
We are PPP connected!!!

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