DB Saver Fare

Train tickets are available for sale 3 months ahead of the departure date. Since there are certain number of tickets allotted for each train at different discount levels, it depends on how popular a given train is. Often you will see higher prices on early morning and late afternoon trains while mid-day and evening trains will be cheaper. And yes, you can sometimes find a "Sparpreis" ticket where 2 traveling together is further discounted. Remember, when you buy a "Sparpreis" ticket, it is for a specific train and is totally nonrefundable, nonchangeable, like an airline ticket.
If it is a relatively short haul, you can get a regional ticket that allows up to 5 traveling together after 9 am (or all day weekends) on regional trains until 3 am the next day for a single discounted price. That does not work with the fast ICE, IC or EC trains. There is also a German wide ticket called a "Quer durchs Land" ticket that is good all over Germany for a bit more. These can be bought right up to train time with no limit on the train capacity. There is no relationship required for the group; friends, relations, whatever. One person buys the ticket and identifies up to 4 other traveling companions.
http://www.bahn.com/i/view/USA/en/prices/germany/savings-fare.shtml
http://www.bahn.com/i/view/USA/en/prices/germany/regional-offers-overview.shtml
There is a similar deal available for Austrian trains.
Trains inside Switzerland are generally not discounted, but trains to/from Germany or Austria and Switzerland do have discounted tickets with restrictions similar to "Sparpreis" tickets.
Also, your German friend may already have a half fare card or student discount card that enables them to travel on their own ticket for a discount.

SparPreis tickets have to be purchased at least 3 days in advance, and there is a surcharge for purchase at a ticket counter. The starting price is 29€ for the first person for any stretch in Germany, using any number of trains, as long as they are booked on one ticket and at least one is an express train (ICE/IC/EC). Starting price for short trips (under 250 km) is 19€. Additional co-travelers pay 9€ less.

The express train(s) are only for the one (date and time) specified on the ticket, but any regional trains can be taken from midnight that day until 10 AM the next morning, as long as it is on the same route specified on the ticket.

The ticket is returnable less a 15€ penalty up to the day before travel; it is nonreturnable as of the day of travel.

Quer-durchs-Land-Tickets are for weekday travel after 9 AM; on weekends you can use the similar Schönes-Wochenende-Ticket all day.

Thank both of you for your answers. It's now beginning to make sense..

Since saver fares have been on sale for a while, some of the best discounts may already be sold out. Go ahead and book soon for any departure date and time that you're committed to for the longer, more expensive routes. I trust that a railpass is not your preference in this case because of the price, not because the travel dates are spread out. For comparison, a Select Saverpass for 5 travel days within 2 months in 4 countries costs about $500 per person in 1st class, but a European resident is not eligible to use this pass with you.

In addition to Savings Fare tickets for long runs on express trains (IEC/IC/EC),

The Quer-durchs-Land-Ticket is 60€ for a group of three people (20€ each) traveling together on regional trains on workdays.

The Schönes-Wochenende-Ticket, on weekend days is 44€ for a group of up to 5 people (less than 15€ each for three).

And in an individual German state (Land), there are Länder-Tickets for travel on regional trains just in that state. An example, in Bavaria, the Bayern-Ticket cost 31€ for three people and is valid all day on weekdays, after 9 AM on workdays. Sometime multiple states are combined, such as the Berlin-Brandenburg-Ticket or the Sachsen, Sachsen-Anhalt, Thüringen Ticket.

And your German friend can join the group.