Just want to know what's the best way to delete all the objects (tables, indexes, squences, etc..) from a tablespace?
Delete the tablespace and recreate it?

Just drop the tables from the User(s) whatever exists in that tablespace.This way u can be sure everything is removed.You don't need to drop the tablespace. If you are using Oracle Enterprise Manager(OEM) its very simple...just click on the database-schema-tables-select all the tables in that user and remove them from the schema....do the same for the views/synonyms/seq...
(OR)
If you are not having OEM then u can write a sql stm to drop the tables/views/synonyms/....from each user individually.
(OR)
If you are not worried about the users and the data in it....simply drop the user which will remove everything.
First list out all the users in that tablespace and proceed.

I do have OEM installed. When I try to run it, it will not let me connect. I'm leaving the management server box blank (the database is local) and using all the different username/password combos I can think of that oracle came with. Am I missing something here?

For logon to OEM u might be using a right password but may be the TNSNAMES.ora file have some issues.Check your sqlnet.ora file and all the tns aliases in the tnsnames.ora file and make sure ur using .world in your host or just the string.
Ex: system/manager@orcl.world --if sqlnet.ora has names.default_domain=world
Ex: system/manager@orcl --if sqlnet.ora dont have any entry or commented for names.default_domain=world
The thing is OEM configures itself with the TNSNAMES.ora once installed so while conecting it only expects you to connect using uname/pwd as the host name is already picked by it.In the worst case create a new database tree and try.