It's possible to acquire a license without speaking any Japanese,; however, things will go much better if you know some keys words and phrases.
Class 1 License 第一種運転免許 (だいいちしゅうんてんめんきょしょ) - The full and proper name for a normal driver's license of ordinary vehicles, mopeds, and special light equipment.
Class 2 License 第二種運転免許 (だいにしゅうんてんめんきょしょ) - Commercial driving licenses.
Driver's License 運転免許証 (うんてんめんきょしょ) - A license to drive a motor vehicle described in Japanese Road Traffic Law 84.
Driving Center 運転免許試験場 (うんてんめんきょしょしけんじょう) - A governmental office where one handles driver's license related matters and takes the tests.
Provisional License 仮運転免許 (かりうんてんめんきょしょ) - A provisional license to drive under the supervision of a qualified instructor, explained in Japanese Road Traffic Law 87.
Moped 原動機付自転車 (げんどうきつきじどうしゃ) - A motorcycle with an engine displacement of 50cc or less.
Ordinary Vehicle 普通自動車 (ふつうじどうしゃ) - An vehicle weighing less than 3500kg, with a load capacity less than 2000kg, and capable carrying 10 or fewer people.
Special Light Equipment 特殊自動車(小型) (とくしゅじどうしゃ(こがた))- Small vehicles, no more than 4.7m long, 17.m wide, or 2.0m high which cannot exceed 15kph. These are things like farm and landscaping equipment.
Technical Test 技能の試験 (ぎのうのしけん) - The practical driving test in a real automobile.
Written Test 学科試験 (がっかしけん) - The written test you take to prove your knowledge, the Provisional and Class 1 Driver's Licenses require these.