The Fleet Status site is:

https://sites.google.com/site/unitedfleetsite/

At the site, you can find information about the interior features, livery, etc., for every plane in United's fleet.

To determine which plane your flight will be on go to mobile.united.com and then click on flight status. Put in the flight number for your flight and just have it use today's date (occasionally it'll say flight not operated on this date in which case just choose one of the other 3 dates it lists). In the address bar you'll see something like this:

mobile.united.com/FlightStatus/FlightDetails?carrierCode=UA&flightNumber=415&flig htDate=9%2F15%2F2015&origin=JFK&destination=SFO

https://mobile.united.com/FlightStatus/FlightDetails?carrierCode=UA&flightNumber=415&flig htDate=9%2F15%2F2015&origin=JFK&destination=SFO

Just change the flight date to match the day of your scheduled flight and then change the origin / destination as necessary. Once you do that look in the details tab under aircraft # and if they have assigned a plane it'll say something like #3506 and the type of plane. Once you know that go to the United Fleet website listed above and cross-reference the four digit number against the "aircraft" column under the appropriate aircraft type.

Keep in mind that things change as they get closer and sometimes either they won't have assigned an aircraft yet or it'll be assigned #0 if it's a few days away and they are anticipating aircraft movement.

You may also check the specific fleet variant of each flight at the United Cargo site under "Schedules & tracking". This data tends to be reliable starting 7 days in advance, but is always subject to change.

United Airlines Equipment (Aircraft) Codes (via JOSECONLSCREW28):

sCO
77Y - B777-200ER (Tail #s 001 - 022)
76P - B767-400ER (Tail #s 051 - 066)
78V - B787-8 (Tail #s 901 - 910, 912, 913)
78Z - B787-9 (Tail #s 950 - 951)
75B - B757-200 AVOD (Tail #s 101 - 141)
75C - B757-300 DirecTV (Tail #s 851 - 859)
75A - B757-300 Overhead IFE (Soon to be streaming content) (Tail #s 860 -871) (Tail #s 860 - 863, 865 have Personal Device Entertainment)
73V - B737-900ER (Tail #s 413 - 478)
73I - B737-900 (Tail #s 401 - 412)
73F - B737-800 DirecTV, Short Field Performance (Tail #s 501 - 518)
73T - B737-800 DirecTV (Tail #s 519 - 531)
73J - B737-800 DirecTV (Tail #s 202 - 226, 228 - 231, 233, 234, 237 - 239, 241 - 245, 247, 248, 250 - 259, 260, 267, 278 - 299.
(Tail #s 260 - 277 will be included here when installed with DirecTV)
73X - B737-800 Mid-Cabin Lav, Overhead IFE (Tail #s 261 - 266, 268 - 277) Will become 73J when installed with DirecTV and mid-cabin lav is removed.
Also known as "midlav" ships.
73M - B737-800 Guam, Overhead IFE (Tail #s 201, 227, 232, 235, 236, 240, 246, 249)
73A - B737-700 Mainland, DirecTV (Tail #s 701 - 719, 721 - 724, 726 - 733, 750)
73P - B737-700 Guam, Overhead IFE (Tail #s 720, 734 - 736)

sUA
19J - A319 (Old Configuration)
19S - A319 (New Configuration) (Slimline Seats)
20B - A320 (Old Configuration 12F/132Y)
20S - A320 (New Configuration 12F/138Y) (Slimline Seats)
20U - A320 (Old Configuration 12F/126Y)
37K - B737-900ER (Tail #s 811 - 848) (Slimline Seats)
47C - B747-400
57Q - B757-200 2-cabin (54xx Tail #s)
57U - B757-200 2-cabin (56xx Tail #s) (Overwater)
67I - B767-300 3-cabin (Tail #s 6441 - 6463) (11 aircraft to become 76E)
73B - B737-900ER (Tail #s 801 - 810)
75J - B757-200 ps (59xx & 53xx Tail #s)
76E - B767-300 2-cabin (Tail #s 6664 - 6677)
77A - B777-200 2-cabin (Tail #s 2510 - 2515) (Non Reconfigured)
77C - B777-200 2-cabin (Tail #s 2368, 2372 & 2379) (Reconfigured)
77D - B777-200 3-cabin (24xx Tail #s)
77H - B777-222 2-cabin (Tail #s 2510 - 2515) (Reconfigured)
77J - B777-200 3-cabin (Tail #s 2704, 2706, 2786, 2791, 2792, 2793, 2795, 2796, 2799)
77Q - B777-200 3-cabin (20xx & 28xx Tail #s)