Arm Swelling or Lymphedema
One of the most annoying side effects after treatment for breast cancer is a swollen arm. (Read the patient advice page here.)  This usually results from obstruction of the small lymphatic vessels due to scarring in the axilla (arm pit) related to treatment of the lymph nodes. Recent review here.

 The best approach to lymphedema is to try to avoid it. The risk of swelling is higher if more extensive surgery is performed and if the axilla is given additional radiation. The patient is encouraged to do gentle range of motion exercises of the arm and shoulder and avoid any additional injury or trauma to the hand or arm (so avoid getting blood drawn from this side, blood pressure measurements, or scratching or cutting the arm or hand.) Patients who develop swelling may benefit from physical therapy, compression stockings or pumps. A recent study from Germany of  over 6,000 women with breast cancer (Meek, Oncology Times, Dec 1998) noted the following:

Risk of Arm Swelling Related to Treatment
Surgery Only   Surg + Radiation  
radical mastectomy 22% radical mastectomy 44%
modified radical mastectomy 19% modified radical 29%
breast conserving 7% breast conservation 10%

In patients treated with breast conservation (lumpectomy) if only axillary dissection alone or axillary radiation alone is used, the risk of swelling is only 2-4%, if the axilla is operated on and also radiated the risk is 9 - 25%

Recent Italian Study (Cancer 2001;92:783)

Treatment cases % with lymphedema
radical mastectomy 306 14.9%
lumpectomy + radiation 732 17.9%
lumpectomy alone 240 11.3%
The American Cancer Society  recently published a symposium issue on breast cancer related lymphedema (Cancer 1998:83/12. December 15,1998) which contains a wealth of information on treating lymphedema. They noted that the incidence of arm swelling ranges from 6-30% (20% average) in recent years. Risk factors include: treatment to the axilla, obesity, hypertension, infections of the arm. The best therapy is not known but a regimen that includes the following is appropriate: skin care,   gentle massage (manual lymph node drainage) compression bandages (and or pumps) and exercise. A recent study (Cancer 2001;92:1368) showed that the two things that were related to developing lymphedema: arm infection/injury and weight gain since surgery. Read the review article the ACS review, the patient advice page here and the more complex review here, and the references below.
a good source of information is the national lymphedema network,  NCI physician and patients infoOncoLink