Later, Clinton, Syrian Foreign Minister Farouk al-Sharaa and Israeli Prime Minister Ehud Barak walked across a pedestrian bridge connecting two sets of buildings at the complex, said Shepherdstown Mayor Vince Parmesano.
All of Monday's talks were to be held at the training center, said U.S. State Department spokesman James P. Rubin.
U.S. Secretary of State Madeleine Albright arrived in Shepherdstown about 9:30 a.m. for the talks, Rubin said during an afternoon press briefing at the college's Frank Arts Center.
The talks began with Clinton meeting privately with Barak and Albright meeting with al-Sharaa, Rubin said. Then Clinton would meet with al-Sharaa and Albright with Barak, Rubin said.
About 520 people are to be involved in the peace talks and Rubin described the discussions as "very high level," even more so than the Wye River Peace Accords, which were held on Maryland's Eastern Shore last year.
Rubin illustrated the point by saying that both sides have brought experts in the fields of law, science and geography to aid in the discussions, Rubin said.
"This is a unique and historic opportunity. No one knows if it will ever come again," Rubin told about 100 reporters, photographers and TV news crew members in the auditorium of the Frank Arts Center. About 215 press credentials were issued to journalists covering the talks.
Rubin said the talks could last more than a week. "I packed for many days," he said, adding jokingly that he didn't want to be forced to go to the area's outlet shops for clothing.
Reporters pressed Rubin for details of the talks, including whether the delegations would use cell phones during the talks or make public appearances in town.
Rubin said the Syrian and Israeli parties agreed to turn off their cell phones during the talks to reduce distractions. Rubin said that might make the reporters' jobs more difficult.
Reporters' cell phones rang periodically throughout Rubin's briefing.
Cell phone communication may not be the best in Shepherdstown anyway, said Rubin, who said he had trouble getting his phone to work in the rural area of Jefferson County.
It is possible that the Israeli and Syrian negotiating teams would visit local attractions to get a break from the talks, Rubin said.
"We're not holding anyone hostage against their will. I expect people to take walks," Rubin said.Local officials reported no problems in town during the first day of talks. Although a special area has been set up in Morgans Grove Park along W.Va. 480 for demonstrations, none had taken place as of late afternoon, said Parmesano.
There was a noticeable feeling of excitement among downtown residents as they talked about the summit and pointed at Marine helicopters buzzing in and out of the college campus. But traffic in town was about average, Parmesano said.
Later in the afternoon, however, traffic became snarled when Clinton's motorcade made a second trip through the area.
Security was tight for the talks. More than 100 federal and local law enforcement officers, some in uniform and some in plain clothes, could be spotted around town, Parmesano said.
There was concern in the community that any protests or acts of terrorism at the Clarion Hotel and Conference Center could spill over to nearby Shepherdstown Junior High School and Shepherdstown Elementary School.
Schmitt, who is also the town recorder, and Parmesano said security was being provided for the schools, although they did not elaborate.
Some parents kept their children out of school Monday due to fears of violence while others took their children out of school to see Clinton, Schmitt and Parmesano said.
"I think when you look in retrospect, this is probably the most secure place in the U.S.," Parmesano said.
Several people who live near Shepherd College said West Virginia State Police officers were out in force Monday morning.
"They checked my ID when I came out of my house," said Carol Marie Didden, who lives on West High Street.
Didden's aunt, Ann Didden, said she was questioned in the morning as she was returning her camper to her sister-in-law's home on Shepherd Grade Road.
"They just told me I have to hurry up. I think I beat Bill (Clinton) by a few minutes," she said.
It was not known whether Clinton would attend today's talks, Rubin said. The location for today's talks also was undetermined, he said.
If talks are going well at the National Conservation Training Center, they could remain there, or they could be moved to the Clarion Hotel and Conference Center if it appears the delegations want to try a different setting, according to Rubin.
Staff writer Brendan Kirby contributed to this story.